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Significant figures

Significant figures of a measurement (number) are the meaningful digits that reflects the resolution of the tool used for that measurement.

Rules to find significant figures of a number

Rule 1: All non-zero digits are significant.

Example: 684 has 3 significant figures (6, 8 and 4).

Rule 2: All zeros between non-zero digits are significant.

Example: 90.08 has 4 significant figures.

Rule 3: Leading zeros (i.e., zeros to the left of the first non-zero digit) are not significant.

Example: 0.00795 has 3 significant figures (7, 9 and 5).
We ignore the leading zeros, because they are used as placeholders.

Rule 4: Trailing zeros (i.e., zeros to the right of the last non-zero digit) are significant only if there is a decimal point.

Example: 80000 has one significant figure (ignore the zeros on the right as there is no decimal point).
74.00 has 4 significant figures (as there is a decimal point).
70.000 has 5 significant figures (as there is a decimal point).

Significant figures rounding rule for addition or subtraction

When you are adding two or more numbers, you need to round the result with correct number of significant numbers. For that, first identify the least accurate number, count its decimal places and round the final result to have this number of decimal places. Same rule applies for subtraction.

Example:You are adding three numbers,

$10.26+5.3+0.002=15.562$

Least accurate number of all the three numbers is 5.3 as it has only one decimal place (i.e., the 3 after the decimal point). So you need to round the result to have one decimal place. Answer is therefore, $15.6$

Significant figures rounding rule for multiplication or division

When you are doing multiplication or division, find how many significant figures each number has, note down the least number of all and round the result to have this number of significant figures.

Example 1: $7.6 \times 10.7 =81.32$

Number 7.6 has 2 significant figures and 10.7 has 3. Out of these, 2 is the lowest, therefore round the answer to have 2 significant figures:

$7.6 \times 10.7 =81$

Example 2: $40/3.0=13.333$

Lowest number of significant figures is 1, the number 40 has. So you must round the answer to 1 significant figure:

$40/3.0=10$