Significant Figures

Significant Figures in Calculations

If sig figs tell us how precise a number is, what happens when we do calculations with them? How many sig figs will be in our final answer?

Addition and subtraction

Write your answer to the decimal point of the last s.f. of the least reliable value.

Examples:

$1200.0cm +\ 12.24cm =\ 1212.24cm \rightarrow 1212.2cm$

$57.23^oC - 273.2^oC + 69^oC = -146.97^oC \rightarrow -147^oC$

Multiplication and division

Write your answer to the same number of s.f. as the value with the least number of s.f.

Examples:

$1200.0cm \times 12.24cm =\ 14688cm \rightarrow 14690cm$

$57.23^oC \times 273.2^oC \div 69^oC = 226.5976...^oC \rightarrow 230^oC$

Examples: Significant Figures

Here are some examples to clarify significant figures.

1. How many significant figures are in the below numbers
2. $1128.01001km$
3. $002.54min$
4. $23.5m/s$
5. $1990K$

2. How many significant figures are in the final answer?

$(2.3 + 23) \times 210.3$

3. How many significant figures are in the final answer?

$\dfrac{\$21.02 + \$1.31}{3\text{ shirts}}$