Rounding and Significant Figures - Numerical Methods Step by Step

Rounding to significant figures keeps a fixed number of meaningful digits regardless of magnitude. Rounding to decimal places fixes the number of digits after the point. Examples: 3.14159 to 4 sig figs is 3.142; 0.0045678 to 3 sig figs is 0.00457; 2.7182818 to 2 decimal places is 2.72.

Example

Round values to the requested significant figures or decimal places.

highlighted = computed this step

Step 1 — Set up

Set up the rounding examples.

\text{Round each value.}

Step 2 — Example 1

Round example 1 to the requested precision.

3.14159 \rightarrow \hlmath{3.142}

Step 3 — Example 2

Round example 2 to the requested precision.

0.0045678 \rightarrow \hlmath{0.00457}

Step 4 — Example 3

Round example 3 to the requested precision.

2.7182818 \rightarrow \hlmath{2.72}

Step 5 — Rounded values

List the rounded results.

\hlmath{3.142} , \hlmath{0.00457} , \hlmath{2.72}

rounding-and-significant-figures To round to N significant figures: locate the Nth significant digit, look at the next digit, round half-even. Leading zeros do not count as significant. Decimal-place rounding counts from the decimal point.