Essential Mathematics

Abstract

Significant figures are the number of digits in a measured or calculated value that are statistically significant or offer reasonable and reliable information. Significant figures in any measurement usually contain digits that are known with certainty and one digit that is uncertain. To determine the number of significant figures, follow these rules. 1. All nonzero digits (1–9) are significant. For example, 125 has 3 significant figures and 14.44 has 4 significant figures. 2. Leading zeros to the left of the first nonzero digit in the number are not significant. They are only used to fix the position of the decimal. For example: • 0.007 has one significant figure • 0.000105 has 3 significant figures • 0.000000000015 has 2 significant figures 3. Zeros between nonzero digits are significant. For example: • 5.005 has 4 significant figures • 50.05 has 4 significant figures • 500.0000075 has 10 significant figures 4. All zeros to the right of the decimal point in a number greater than 1 are significant. For example: • 25.00 has 4 significant figures • 0.1250 has 4 significant figures • 0.2000 has 4 significant figures 5. Zeros at the end of a number may or may not be significant. They are significant only if there is a decimal point in the number. For example: • 1500 has 2 significant figures • 1500. has 4 significant figures • 602,000,000,000,000,000,000,000 has 3 significant figures • 404,570,000 has 5 significant figures • 404,590,000. has 9 significant figures Rounding off is a process of eliminating nonsignificant digits from a calculated number. The rules governing rounding off are summarized below: 1. If the nonsignificant digit is less than 5, round it and all digits to its right off. For example, 100.5129 is equal to 100.5 if rounded off to 4 significant figures. 2. If the nonsignificant digit to the right of the last digit to be retained is a 5 followed by zeros, the last digit is increased by one if it is odd, and is left unchanged if it is even. For example, 64.750 is 64.8 to 3 significant digits, but 25.850 is 25.8 to 3 significant figures.