Significant Figures and Rounding

Significant figures: meaningful digits in a measured quantity.


1. Any digit that is not zero is significant. 1234.56 6 significant figures

1234.56 6 significant figures

2. Zeros between non-zero digits are significant.

1002.5 5 significant figures

3. Zeros to the left of the first non-zero digit are not significant.

000456 3 significant figures
0.0056 2 significant figures

4. If the number is greater than one (1), then all zeros to the right of the decimal point are significant.

457.12 5 significant figures
400.00 5 significant figures

5. If the number is less than one, then only zeros that are at the end of the number and between non-zero digits are significant.

0.01020 4 significant figures

6. For numbers that do not contain decimal points, the trailing zeros may or may not be significant. In this course assume the digits are significant unless told otherwise.

1000 1, 2, 3, or 4 significant figures. UNCLEAR assume 4 in calculation
0.0010 2 significant figures
1.000 4 significant figures

7. Assume defined and counted quantities have an unlimited number of significant figures.

NOTE: It is much easier to count and keep track of significant figures if the number is written in scientific notation.

Use in calculations

1. Addition & Subtraction: The number of significant figures to the right of the decimal point in the final sum or difference is determined by the lowest number of significant figures to the right of the decimal point in any of the original numbers.

6.2456 + 6.2 = 12.4456 rounded to 12.4 note: 3 significant figures in answer

2. Multiplication & Division: The number of significant figures in the final product or quotient is determined by the original number that has the smallest number of significant figures.

2.51 x 2.30 = 5.773 rounded to 5.77
2.4 x 0.000673 = 0.0016152 rounded to 0.0016

Rounding

1. Drop the digits that follow the last significant digit if the first digit is less than 5.

Round 1.61562 to 2 significant figures ANS: 1.6

2. If the first digit to be dropped is greater than five, increase the preceding digit by 1.

Round 1.61562 to 5 significant figures ANS: 1.6156

3. If the first digit to be dropped is five and there are non-zero digits following the five, increase the preceding digit by 1.

Round 1.61562 to 3 significant figures ANS: 1.62
Round 1.62500003 to 3 significant figures ANS: 1.63

4. If the fist digit to be dropped is five and there are only zeros following the five, round to the even number.

Round 1.655000 to 3 significant figures ANS: 1.66
Round 1.625000 to 3 significant figures ANS: 1.62

5. BE CONSISTENT IN YOUR ROUNDING.