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Significant figures

The digit in a number which best indicates its size is known as the ‘first significant figure’. It is always the first non zero digit in the number.

Significant figure is often abbreviated to sig. fig. or s.f.

For the number 6572, ‘6’ is the first significant figure because it tells us that the number is 6 thousand and something.

‘5’ is the second sig. fig. as it tells us the number is 6 thousand and 5 hundred.

‘7’ is the third sig. fig. and ‘2’ is the fourth.

For the number 0.00301, ‘3’ is the first sig. fig. as it tells us that the number is 3 thousandths and something.

The first 3 zeros are not counted as significant but the zero between the ‘3’ and ‘1’ is the second sig. fig. ‘1’ is the third sig. fig.

Answers to calculations are often rounded to a number of significant figures, usually 1, 2 or 3.
Normal rules for rounding apply.

Round up if the digit to the right is 5 or more; otherwise leave that digit as it is.

Example

Round 378.65 to 1 significant figure.

Solution:

The first sig. fig. is 3. The digit to the right is 7 so we need to add 1 to the 3.
378.65 rounded to 1 significant figure is 400

The answer should be approximately the same as the original number.

Answer

400

Example

Round 378.65 to 3 significant figures.

Solution:

The third sig. fig. is 8. The digit to the right is 6 so we need to add 1 to the 8. 378.65 rounded to 3 significant figures is 379

Answer

379

Example

Round 0.0080732 to 3 significant figures.

Solution:

The third sig. fig. is 7.
(Remember – don’t count the zeros before the first sig. fig.) The digit to the right is 3 so we leave it as it is. 0.0080732 to 3 significant figures is 0.00807

Answer

0.00807