Magnitude Of Number Research Articles

Changes in Phyto- and Zooplankton under the Climatic Shifts and Anthropogenic Load (Lake Baikal, Russia)

The hydro-chemical data collected today and structural and quantitative parameters of phyto- and zooplankton from Maloe More Strait, Lake Baikal, were analysed. Comparison of current and earlier observations revealed recent alterations in phyto- and zooplankton functions analogous to other areas of Lake Baikal. Major reconstructions in phytoplankton were registered in spring: violation in cycles of annual growth maxima of large-cell Baikalian diatoms and changes in dominant species. Dramatic abundance of rotifers caused the increase by an order of magnitude in pelagic zooplankton numbers in 2019–2020. In 2021, all of these groups were suppressed under intensive diatom vegetation. In the Mukhor bay, such changes were related to a sharp increase of rotifer numbers until 2021. In 2021, we observed decline in plankton abundance, meanwhile the relative proportion of taxonomic groups did not change with dominance of rotifers.

Darcy-Forchheimer flow of bioconvective nanofluid over a nonaligned stretching surface with slip effects

The primary objective of this investigation is to explore the effects of velocity and nanoparticle slip mechanism on the hydrodynamic behavior of the Darcy-Forchheimer flow of nanomaterials where the blend of (Fe2O3−H2O) (50%−50%) was used as a working fluid. The bioconvection flow of multi-diffusive nanofluid fluid across sheet surface is investigated taking the consequences of oxytactic microorganisms. The Brownian motion and thermophoretic phenomena is explored using Buongiorno slip mechanism theory while the Tiwari Das model incorporate the volume percentage of nanoparticles. The Darcy-Forchheimer medium appears at the sheet surface that permits the flow in the horizontal direction with the effects of permeability and drag. The flow is subjected to first and second order slip and radiative heat transfer. The action of gyrotactic microbes is supported by bioconvection, which strengthens the phenomena of mass transfer. The fundamental governing equations resulting from computational modelling are turned into ordinary differential equations using suitable rescaling variables. The identified complicated equation was numerically solved using the Runge-Kutta-Fehlberg fourth order procedure with shooting techniques. The volume friction of the nanoparticles and the Knudsen number accelerate the stretching and nonaligned velocities field of the nanofluid. The Darcy number, on the other hand, slows down the velocities near the sheet surface. The temperature profile rises against thermal radiation and volumetric friction, while an inverse tendency is found with higher Prandtl number magnitude. The concentration profile of nanoparticles advances through the thermophoresis parameter. The bioconvection Lewis number and the Peclet number shrink the density profile of gyrotactic motile microbes.

A trial solution for imposing boundary conditions of partial differential equations in physics-informed neural networks

This article proposes an auxiliary function for imposing the boundary and initial conditions in physics-informed neural network models in a hard manner that accelerates the learning process. This auxiliary function consists of two pre-trained neural networks and a main deep neural network with trainable parameters. The novelty of this new auxiliary function is the input of main deep neural network, which takes the outputs of distance function and boundary function as inputs in addition to the spatiotemporal variables. We demonstrate the efficacy and general applicability of the proposed model by applying it to several benchmark-forward problems namely, advection, Helmholtz and Klein-Gordon equations. The accuracy of predictions is examined by comparison with exact solutions. Our findings imply the superiority of the proposed model because of the improvement of the loss convergence to lower values by one order of magnitude for the same number of epochs. In the case of the advection equation, the relative L2 error has been reduced from 0.025 to 0.0201, and from 0.016 to 0.0152. When applied to the Helmholtz equation, our novel model achieved an error of 8.67 × 10−3, surpassing the conventional model's performance, which yielded an error of 6.04 × 10−2. Furthermore, for the Klein-Gordon equation, our new model led to a remarkable reduction in the relative L2 error, from 0.18 to an impressive 4.2 × 10−2.

Rheological behaviour of Carreau liquid past a wedge surface with binary chemical reaction

The time-dependent stream of rheological Carreau nanoliquid carrying microbes through a rotating lodge through porous media in addition to irregular heat source or sink characteristics is the subject of this article. Due to the fact that the Carreau liquid can reveal the rheology of liquids with short-chain suspended particles, liquid crystals, surfactants, and human and animal blood, it is helpful to depict a range of physical problems. The influence of infinite shear rate thickness is combined to provide the mathematical formulation. Both the static and moving physical features are covered in great depth. Prior to using the finite element technique to solve revised equations numerically, pertinent similarity transformations are used to get equations in their dimensionless form. According to the findings of our study, the temperature and the thickness of the thermal boundary layer that corresponds to that temperature both improves the function that the thermal radiation factor plays in shear thickening and thinning liquids. Additionally, a moving wedge has a greater velocity than a static wedge. The thermophoresis factor's rising function is the concentration field. Furthermore, by increasing the Piclet number's magnitudes, the profile of microbes is diminished.

MHD nanofluid flow through Darcy medium with thermal radiation and heat source

In this analysis, we have considered heat transmission in two-dimensional steady laminar nanofluid flow past a wedge. Magnetohydrodynamic (MHD), Brownian motion, viscous dissipation and thermophoresis effects are considered over the porous surface. Similarity transformations have been used to change the governing partial differential equations (PDEs) into nonlinear higher-order ordinary differential equations (ODEs). Governing ODEs with boundary conditions are then converted to the system of first-order initial value problem. After that the modeled system is solved numerically by RK4 technique. Impact of the magnetic number, Eckert number, Prandtl number, Lewis number, Brownian motion, thermophoresis and permeability parameters on the flow domain is analyzed graphically as well as in tabular form. It is noted that magnitude of Nusselt number for the flow regime increases with the increase of nondimensional parameter [Formula: see text] while opposite behavior is observed in case of R.

Competing numerical magnitude codes in decimal comparison: Whole number and rational number distance both impact performance

A critical difference between decimal and whole numbers is that among whole numbers the number of digits provides reliable information about the size of the number, e.g., double-digit numbers are larger than single-digit numbers. However, for decimals, fewer digits can sometimes denote a larger number (i.e., 0.8 > 0.27). Accordingly, children and adults perform worse when comparing such Inconsistent decimal pairs relative to Consistent pairs, where the larger number also has more digits (i.e., 0.87 > 0.2). Two explanations have been posited for this effect. The string length congruity account proposes that participants compare each position in the place value system, and they additionally compare the number of digits. The semantic interference account suggests that participants additionally activate the whole number referents of numbers – the numbers unadorned with decimal points (e.g., 8 < 27) – and compare these. The semantic interference account uniquely predicts that for Inconsistent problems with the same actual rational distance, those with larger whole number distances should be harder, e.g., 0.9 vs. 0.81 should be harder than 0.3 vs. 0.21 because 9 < < 81 whereas 3 < 21. Here we test this prediction in two experiments with college students (Study 1: n = 58 participants, Study 2: n = 78). Across both, we find a main effect of consistency, demonstrating string length effects, and also that whole number distance interferes with processing conflicting decimals, demonstrating semantic interference effects. Evidence for both effects supports the semantic interference account, highlighting that decimal comparison difficulties arise from multiple competing numerical codes. Finally, for accuracy we found no relationship between whole number distance sensitivity and math achievement, indicating that whole number magnitude interference affects participants similarly across the spectrum of math achievement.

Relative Influences of Inertia and Polymeric Viscoelastic Effects on Nusselt Numbers within Rotating Couette Flows

In past investigations of elastic instabilities and elastic turbulence, almost no attention has been devoted to the effects and influences of inertial phenomena. Within the present investigation, Nusselt number data are provided to illustrate the relative influences of inertia and polymeric viscoelastic phenomena within a rotating Couette flow (RCF) environment. Data are provided from experimental measurements of local surface heat transfer characteristics for different flow passage heights, one radial position, and different values of disk rotational speed for polyacrylamide polymer concentrations ρ of 0 ppm, 100 ppm, 150 ppm, and 300 ppm. With this approach, data for a wide range of shear rate γ˙ values, Weissenberg numbers, and first normal stress difference values are provided. Nusselt number data are provided as dependent upon a newly developed P′ parameter, equal to ReEI/Re0.22, which collapse into a single distribution over the range of P′ values considered which range from 0 to about 182. Such characteristics indicate that the P′ parameter provides an appropriate means to simultaneously account for the relative influences of inertia and polymeric viscoelastic effects. The use of such a power law dependence for Re additionally gives P′ values which are dominated by ReEI values when the Weissenberg number Wi is greater than the elastic instability transition onset value. The experimental conditions associated with this value correspond to the change from inertia domination (with buoyance influences) to polymeric viscoelastic domination which occurs for shear rates in the vicinity of 11 to 12 s−1. For Weissenberg numbers greater than the onset value, Nusselt numbers associated with H = 5 mm are generally the highest values measured, with magnitudes that steadily increase with γ˙. Associated Nusselt numbers become as high as about 3.0, whereas zero-shear rate values (obtained with zero rotation) are in the vicinity of 1.0. At lower Weissenberg number magnitudes (below the transition onset value), Nusselt numbers cover a wide range of values as experimental conditions and configuration are varied, as a consequence of the complicated and simultaneous influences of inertia, buoyancy, and dilute polymer presence.

Efficient Robustness Assessment via Adversarial Spatial-Temporal Focus on Videos.

Adversarial robustness assessment for video recognition models has raised concerns owing to their wide applications on safety-critical tasks. Compared with images, videos have much high dimension, which brings huge computational costs when generating adversarial videos. This is especially serious for the query-based black-box attacks where gradient estimation for the threat models is usually utilized, and high dimensions will lead to a large number of queries. To mitigate this issue, we propose to simultaneously eliminate the temporal and spatial redundancy within the video to achieve an effective and efficient gradient estimation on the reduced searching space, and thus query number could decrease. To implement this idea, we design the novel Adversarial spatial-temporal Focus (AstFocus) attack on videos, which performs attacks on the simultaneously focused key frames and key regions from the inter-frames and intra-frames in the video. AstFocus attack is based on the cooperative Multi-Agent Reinforcement Learning (MARL) framework. One agent is responsible for selecting key frames, and another agent is responsible for selecting key regions. These two agents are jointly trained by the common rewards received from the black-box threat models to perform a cooperative prediction. By continuously querying, the reduced searching space composed of key frames and key regions is becoming precise, and the whole query number becomes less than that on the original video. Extensive experiments on four mainstream video recognition models and three widely used action recognition datasets demonstrate that the proposed AstFocus attack outperforms the SOTA methods, which is prevenient in fooling rate, query number, time, and perturbation magnitude at the same time.

Estuarine Mixing Patterns and Siltation Impact: A Case Study of Air Rami River Estuary

Investigating the Air Rami River Estuary in Mukomuko Regency, this study examines the influence of siltation on mixing characteristics within the estuarine environment. The research aims to discern and characterize mixing patterns in the estuary, employing direct field measurements conducted during both tide and low tide conditions in March 2023. Descriptive and quantitative analyses reveal notable salinity variations, with tidal conditions exhibiting a peak salinity of 10 ppt at a depth of 2 meters, and low tide conditions showing a maximum salinity of 5 ppt at 1.5 meters depth. Temperature variations are also observed, with tide conditions reaching 31.5°C and low tide conditions at 27.2°C. Calculation of the estuary number indicates a perfectly mixed stratified estuary mixing type, characterized by an estuary number magnitude of 0.53. These findings offer insights into estuarine mixing dynamics and their implications for coastal ecosystems.&#x0D; Highlight:&#x0D; &#x0D; Siltation Impact: Investigates the influence of siltation on mixing patterns in the Air Rami River Estuary, Mukomuko Regency.&#x0D; Salinity and Temperature Variations: Describes notable variations in salinity and temperature during tide and low tide conditions, providing insights into estuarine dynamics.&#x0D; Estuary Number Analysis: Utilizes the estuary number to classify estuarine mixing type, revealing a perfectly mixed stratified estuary with implications for coastal ecosystems.&#x0D; &#x0D; Keyword: Estuarine Mixing, Siltation Influence, Salinity Variations, Temperature Dynamics, Coastal Ecosystems

Quantitative Prediction of Sling Events in Turbulence at High Reynolds Numbers.

Collisional growth of droplets, such as occurring in warm clouds, is known to be significantly enhanced by turbulence. Whether particles collide depends on their flow history, in particular on their encounters with highly intermittent small-scale turbulent structures, which despite their rarity can dominate the overall collision rate. Here, we develop a quantitative criterion for sling events based on the velocity gradient history along particle paths. We show by a combination of theory and simulations that the problem reduces to a one-dimensional localization problem as encountered in condensed matter physics. The reduction demonstrates that the creation of slings is controlled by the minimal real eigenvalue of the velocity gradient tensor. We use fully resolved turbulence simulations to confirm our predictions and study their Stokes and Reynolds number dependence. We also discuss extrapolations to the parameter range relevant for typical cloud droplets, showing that sling events at high Reynolds numbers are enhanced by an order of magnitude for small Stokes numbers. Thus, intermittency could be a significant ingredient in the collisional growth of rain droplets.

Simulations for MHD mixed convection in a partially heated lid-driven chamfered enclosure

This study investigates the hydrodynamic convective heat transport mechanism in a chamfered square-shaped cavity filled with water. The upper edge of the cavity is presumed to be at low temperature and moving with constant speed. The mean position of the lower boundary is at higher temperature. The chamfered parts and the remaining edges of the enclosure are thermally isolated and fixed. The flow situation and heat distribution experience variations in response to different magnetic field orientations. This physical configuration exhibits mathematical translation via partial differential equations, which are solved numerically using the Galerkin finite element technique. The findings after simulation are visualized through contour plots and line graphs. The primary goal of this research is to examine the effects of Grashof number, Reynolds number, magnetic field strength, and inclination angle on the flow field and temperature distribution. Our findings provide valuable insights into the mechanisms of mixed convection and heat transfer in chamfered square-shaped cavities under the influence of magnetic fields. It is noted that magnitude of Nusselt number versus Reynolds number decrease from to as Hartmann number increases from to The enhancement in Nusselt number magnitude from upto is aloso observed when Reynolds number rises from upto

Testing the whole number interference hypothesis: Contributions of inhibitory control and whole number knowledge to fraction understanding.

The present study tests two predictions stemming from the hypothesis that a source of difficulty with rational numbers is interference from whole number magnitude knowledge. First, inhibitory control should be an independent predictor of fraction understanding, even after controlling for working memory. Second, if the source of interference is whole number knowledge, then it should hinder fraction understanding. These predictions were tested in a racially and socioeconomically diverse sample of U.S. children (N = 765; 337 female) in Grades 3 (ages 8-9), 5 (ages 10-11), and 7 (ages 12-13) who completed a battery of computerized tests. The fraction comparison task included problems with both shared components (e.g., 3/5 > 2/5) and distinct components (e.g., 2/3 > 5/9), and problems that were congruent (e.g., 5/6 > 3/4) and incongruent (e.g., 3/4 > 5/7) with whole number knowledge. Inhibitory control predicted fraction comparison performance over and above working memory across component and congruency types. Whole number knowledge did not hinder performance and instead positively predicted performance for fractions with shared components. These results highlight a role for inhibitory control in rational number understanding and suggest that its contribution may be distinct from inhibiting whole number magnitude knowledge. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Heat and mass transfer for MHD nanofluid flow on a porous stretching sheet with prescribed boundary conditions

A theoretical study is conducted in order to scrutinize the thermodynamic first law of the MHD nanofluid flow with an inclined magnetic field, radiation, heat source/sink, viscous dissipation, Joule heating, concentration power-law exponent, and the chemical reaction on a porous stretching surface immersed within a permeable Darcian medium. Cobalt ferrite nanoparticles (CoFe2O4) have been combined with pure water to form a nanofluid called CoFe2O4/H2O. The controlling mathematical equations for MHD nanofluid flow are transformed through similarity transformation into non-dimensional equations. The exact solutions for the energy and mass transfer equations are provided in terms of confluent hypergeometric function. The effects of controlling parameters on the velocity, temperature, and concentration profiles are discussed and illustrated with figures and tables. According to the results, increasing the concentration power-law exponent yields a rise in the Sherwood number (PSC) magnitude and the wall concentration (PMF). Furthermore, the 3-D plots showed that the skin friction coefficient is directly related to the Hartmann number, suction parameter, and nanoparticle volume fraction parameter.

Numerical computation of Brownian motion and thermophoresis effects on rotational micropolar nanomaterials with activation energy

The current article investigates the numerical study of the micropolar nanofluid flow through a 3D rotating surface. This communication may manipulate for the aim such as the delivery of the drug, cooling of electronic chips, nanoscience and the fields of nanotechnology. The impact of heat source/sink is employed. Brownian motion and thermophoresis aspects are discussed. The rotating sheet with the impacts of Darcy-Forchheimer law is also scrutinized. Furthermore, the influence of activation energy is analyzed in the current article. The numerical analysis is simplified with the help of befitted resemblance transformations. The succor of the shooting algorithm with built-in solver bvp4c MATLAB software is used for the numerical solution of nonlinear transformed equations. The consequences of different physical factors on the physical engineering quantities and the subjective fields were examined and presented. According to outcomes, it can be analyzed that the flow profile declined with the rotational parameter. It is observed that angular velocity diminishes via a larger porosity parameter. Furthermore, the temperature gradient is declined via a larger magnitude of the Prandtl number. The heat transfer is enhanced in the occurrence of Brownian motion. The activations energy parameter causes an increment in the volumetric concentration field. Moreover, the local Nusselt number is reduced via a greater estimation of the porosity parameter.

Forecasting small-scale dynamics of fluid turbulence using deep neural networks

Turbulence in fluid flows is characterized by a wide range of interacting scales. Since the scale range increases as some power of the flow Reynolds number, a faithful simulation of the entire scale range is prohibitively expensive at high Reynolds numbers. The most expensive aspect concerns the small-scale motions; thus, major emphasis is placed on understanding and modeling them, taking advantage of their putative universality. In this work, using physics-informed deep learning methods, we present a modeling framework to capture and predict the small-scale dynamics of turbulence, via the velocity gradient tensor. The model is based on obtaining functional closures for the pressure Hessian and viscous Laplacian contributions as functions of velocity gradient tensor. This task is accomplished using deep neural networks that are consistent with physical constraints and explicitly incorporate Reynolds number dependence to account for small-scale intermittency. We then utilize a massive direct numerical simulation database, spanning two orders of magnitude in the large-scale Reynolds number, for training and validation. The model learns from low to moderate Reynolds numbers and successfully predicts velocity gradient statistics at both seen and higher (unseen) Reynolds numbers. The success of our present approach demonstrates the viability of deep learning over traditional modeling approaches in capturing and predicting small-scale features of turbulence.

Investigation into the effects of hydrophobicity on thermohydraulic characteristics and entropy generation of hybrid nanofluid with the magnetic property in a micro-heat sink under a magnetic field

The cooling of devices is a big challenge in the electronics industry, and most process units (graphical are central process units) experience defects under harsh temperature conditions, so dissipating generated heat under various working conditions should be studied seriously. This study investigates the magnetohydrodynamics of hybrid ferro-nanofluids in the presence of hydrophobic surfaces in a micro-heat sink. To scrutinize this study, a finite volume method (FVM) is applied. The ferro-nanofluid includes water as a base fluid and multiwall carbon nanotubes (MWCNTs) and Fe3O4 as nanoadditives, which are used in three concentrations (0, 1, and 3%). Other parameters such as the Reynolds number (5–120), Hartmann number (magnitude of the magnetic field from 0 to 6), and hydrophobicity of surfaces are scrutinized for their impacts on heat transfer and hydraulic variables as well as entropy generation variables. The outcomes indicate that increasing the level of hydrophobicity in surfaces leads simultaneously to improved heat exchange and reduced pressure drop. Likewise, it decreases the frictional and thermal types of entropy generation. Intensifying the magnitude of the magnetic field enhances the heat exchange as much as the pressure drop. It can also decrease the thermal term in entropy generation equations for the fluid, but increase the frictional entropy generation and adds a new term, magnetic entropy generation. Incrementing the Reynolds number improves the convection heat transfer parameters, although it intensifies the pressure drop in the length of the channel. Also, the thermal entropy generation and frictional entropy generation decrease and increase with an increasing flow rate (Reynolds number).

Overload in a Rat In Vivo Model of Synergist Ablation Induces Tendon Multiscale Structural and Functional Degeneration.

Tendon degeneration is typically described as an overuse injury with little distinction made between magnitude of load (overload) and number of cycles (overuse). Further, in vivo, animal models of tendon degeneration are mostly overuse models, where tendon damage is caused by a high number of load cycles. As a result, there is a lack of knowledge of how isolated overload leads to degeneration in tendons. A surgical model of synergist ablation (SynAb) overloads the target tendon, plantaris, by ablating its synergist tendon, Achilles. The objective of this study was to evaluate the structural and functional changes that occur following overload of plantaris tendon in a rat SynAb model. Tendon cross-sectional area (CSA) and shape changes were evaluated by longitudinal MR imaging up to 8 weeks postsurgery. Tissue-scale structural changes were evaluated by semiquantified histology and second harmonic generation microscopy. Fibril level changes were evaluated with serial block face scanning electron microscopy (SBF-SEM). Functional changes were evaluated using tension tests at the tissue and microscale using a custom testing system allowing both video and microscopy imaging. At 8 weeks, overloaded plantaris tendons exhibited degenerative changes including increases in CSA, cell density, collagen damage area fraction (DAF), and fibril diameter, and decreases in collagen alignment, modulus, and yield stress. To interpret the differences between overload and overuse in tendon, we introduce a new framework for tendon remodeling and degeneration that differentiates between the inputs of overload and overuse. In summary, isolated overload induces multiscale degenerative structural and functional changes in plantaris tendon.

Modeling visceral leishmaniasis and tuberculosis co-infection dynamics

The co-infection of visceral leishmaniasis (VL) and tuberculosis (TB) patients pose a major public health challenge. In this study, we develop a mathematical model to study the transmission dynamics of VL and TB co-infection by first analyzing the VL and TB sub-models separately. The dynamics of these sub-models and the full co-infection model are determined based on the reproduction number. When the associated reproduction number (R1) for the TB-only model and (R2) for the VL-only are less than unity, the model exhibits backward bifurcation. If max{R1,R2}=R1, then the TB-VL co-infection model exhibits backward bifurcation for values of R1. Furthermore, if max{R1,R2}=R2, and by choosing the transmission probability, βL as the bifurcation parameter, then the phenomenon of backward bifurcation occurs for values of R2. Consequently, the full model, whose associated reproduction number is R0, also exhibits backward bifurcation when R0=1. The equilibrium points and their stability for the models are determined and analyzed based on the magnitude of the respective reproduction numbers. Finally, some numerical simulations are presented to show the reliability of our theoretical results.

Comparative analysis between copper ethylene-glycol and copper-iron oxide ethylene-glycol nanoparticles both experiencing Coriolis force, velocity and temperature jump

Sequel to the industrial usage of ethylene-glycol conveying copper nanoparticles, nothing is known on how the dynamics differ from ethylene-glycol conveying copper and iron oxide nanoparticles when there is Coriolis force, slip and thermal jump. This report presents the outcome of a study on the motion and heat transfer across both non-Newtonian electro-conducting Carreau hybridized nanofluids via the porous medium on a three-dimensional rotating stretchable plate. The model for hybridization of the mixture of copper (Cu) and Iron oxide (Fe3O4) nanoparticles in the ethylene-glycol base fluid under thermal radiation, uneven heat source and wall slip attributes were developed and presented. The reduction of the model equations from partial into ordinary differential equations was carried out using similarity transformation variables. Pseudo-Spectral Method (PSM) was employed to solve the emerged boundary value problem. Exponential space-based heat source/sink, stretching rates, and temperature jump levels, heat transfer rates are maximal during ethylene-glycol conveying copper nanoparticles but minimal during ethylene-glycol motion conveying copper and iron oxide nanoparticles. The hybridization of the nanoparticles induces a higher heat propagation than the unitary nanofluid for all the physical parameters considered, whereas the strength of the surface drag force depreciates with a higher magnitude of the Weissenberg number.

Developmental trajectories of numerical magnitude representations of fractions and decimals.

We examined the development of numerical magnitude representations of fractions and decimals from fourth to 12th grade. In Experiment 1, we assessed the rational number magnitude knowledge of 200 Chinese fourth, fifth, sixth, eighth, and 12th graders (92 girls and 108 boys) by presenting fraction and decimal magnitude comparison tasks as well as fraction and decimal 0-1 and 0-5 number line estimation tasks. Magnitude representations of decimals became accurate earlier, improved more rapidly, and reached a higher asymptotic accuracy than magnitude representations of fractions. Analyses of individual differences revealed positive relations between the accuracy of decimal and fraction magnitude representations at all ages. In Experiment 2, we presented an additional set of 24 fourth graders (14 girls and 10 boys) with the same tasks but with the decimals that were being compared varying in the number of decimal digits. The decimal advantage continued to be present for both magnitude comparison and estimation tasks, indicating that the greater accuracy with decimals was not limited to decimals with equal numbers of decimal digits, though unequal numbers of decimal digits did impact performance with decimals on both magnitude comparison and number line estimation tasks. Implications for understanding numerical development and education are discussed. (PsycInfo Database Record (c) 2023 APA, all rights reserved).