With an increasing demand for power-hungry data-intensive computing, design methodologies with low power consumption are increasingly gaining prominence in the industry. Most of the systems operate on critical and noncritical data both. An attempt to generate a precision result results in excessive power consumption and results in a slower system. For noncritical data, approximate computing circuits significantly reduce the circuit complexity and hence power consumption. In this paper, a novel approximate single precision floating point adder is proposed with an approximate mantissa adder. The mantissa adder is designed with three 8-bit full adder blocks. In this paper, a detailed mathematical background, and proposed design approach in terms of the circuit configuration and truth tables are discussed. Additionally, a concept of switching between exact computing and approximate computing is analysed considering an approximate carry look-ahead adder. The delay and power consumption for the exact operating mode and approximate operation mode considering varied window sizes is observed. Performance of the approximate computation is compared against exact computation and varied approximate computing approaches.