# Significant figures

The significant figures of a given number are those significant or important digits, which convey the meaning according to its accuracy. For example, 6.658 has four significant digits. These substantial figures provide precision to the numbers. They are also termed as significant digits.

Rules for Significant Figures

• All non-zero digits are significant. 198745 contains six significant digits.
• All zeros that occur between any two non-zero digits are significant. For example, 108.0097 contains seven significant digits.
• All zeros that are on the right of a decimal point and also to the left of a non-zero digit is never significant. For example, 0.00798 contained three significant digits.
• All zeros that are on the right of a decimal point are significant, only if, a non-zero digit does not follow them. For example, 20.00 contains four significant digits.
• All the zeros that are on the right of the last non-zero digit, after the decimal point, are significant. For example, 0.0079800 contains five significant digits.
• All the zeros that are on the right of the last non-zero digit are significant if they come from a measurement. For example, 1090 m contains four significant digits.

Rounding Significant Figures

A number is rounded off to the required number of significant digits by leaving one or more digits from the right. When the first digit in left is less than 5, the last digit held should remain constant. When the first digit is greater than 5, the last digit is rounded up. When the digit left is exactly 5, the number held is rounded up or down to receive an even number. When more than one digit is left, rounding off should be done as a whole instead of one digit at a time.

There are two rules to round off the significant numbers:

1. First, we have to check, up to which digit the rounding off should be performed. If the number after the rounding off digit is less than 5, then we have to exclude all the numbers present on the right side.
2. But if the digit next to the rounding off digit is greater than 5, then we have to add 1 to the rounding off digit and exclude the other numbers on the right side.

Significant Figures Examples

Identify the number of significant digits/figures in the following given numbers.

Solution:

 Number Number of Significant digits/figures 450 Two 0.046 Two 8.4320 Five 3202 Four 3400 Two

Significant figures in algebraic operations

During the algebraic operations of addition, subtraction, multiplication and division, the result contains the minimum number of significant figures in the component measurements.

 NOTE 1. The powers of 10 and the zeroes on the left side of the measurement are not counted while counting the significant figures. 2. Greater the number of significant figures in a measurement, smaller is the percentage error. 3. For rounding off significant figures, if the succeeding figure is greater than 5 then the figure is increased by 1 else it is left unchanged.  However, if the succeeding figure is 5 itself then the figure is raised by 1 if it is odd and left unchanged it is even.

Example:      Add 17.35 g, 25.6 g; and 8.498 g and write the result with the correct number of significant figures.

Solutions:    Out of the three given values of mass 25.6 g is least accurate, being correct only upto first place of decimal.  The other two values of mass have to be rounded off to one place of decimal i.e.