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← Levels of Accuracy

Method

Rounding to Significant Figures

Rounding a number to

n

significant figures means to rewrite the number so that it has exactly

n

significant figures. The result is an approximation of the number.

The number $6213.4983$ rounded to three significant figures becomes $6.21 \times 1 0^{3} .$

The following steps should be followed to round a number to

n

significant figures.

Look For the

n th

Significant Figure

Consider the number $6213.4983 .$ In each column, the corresponding significant figure is highlighted.

Round to Three Significant Figures	Round to Five Significant Figures	Round to Six Significant Figures
$6213.4983$	$6217.3983$	$6217.3983$

Draw a Vertical Bar to the Right of This Digit

Round to Three Significant Figures	Round to Five Significant Figures	Round to Six Significant Figures
$621 ∣ 3.4983$	$6213.4 ∣ 983$	$6213.49 ∣ 83$

Look at the Digit to the Right of the Bar

If it is less than $5,$ keep the $n th$ digit the same.

If it is $5$ or more, increase the $n th$ digit by $1 .$
- If the $n th$ digit becomes $10,$ write $0$ instead and increase the previous digit by $1 .$ Repeat this as many times as needed.

Round to Three Significant Figures	Round to Five Significant Figures	Round to Six Significant Figures
$621 ∣ 3.4983 ↓ 621 ∣ 3.4983$	$6213.4 ∣ 983 ↓ 6213.5 ∣ 983$	$6213.49 ∣ 83 ↓ 6213.4 \underline{10} ∣ 83 ↓ 6213.50 ∣ 83$

Look at the Digits to the Right of the

n th

Significant Figure

Remove the bar.
From the $n th$ digit, any digit to the left of the decimal point must be replaced with zero.
From the $n th$ digit, any digit to the right of the decimal point must be removed.

The following table shows the results of rounding $6203.4983$ to $3,$ $5,$ and $6$ significant figures.

Round to Three Significant Figures	Round to Five Significant Figures	Round to Six Significant Figures
$621 3.4983 ↓ 6210$	$6213.5983 ↓ 6213.5$	$6213.5083 ↓ 6213.50$

Extra

When The Rounded Number Has Fewer Digits Than the Original

It may happen that rounding a number results in an integer with fewer digits than the number of digits of the integer part of the original number. In this case, a bar is drawn above the last significant digit to indicate that there were more significant digits.

Rounding the Number $43346$ to
Two Significant Figures	Three Significant Figures	Four Significant Figures
$4 \overset{ˉ}{3} 000$ or $4.3 \times 1 0^{4}$	$43 \overset{ˉ}{3} 00$ or $4.33 \times 1 0^{4}$	$433 \overset{ˉ}{5} 0$ or $4.335 \times 1 0^{4}$

Alternatively, writing the number using scientific notation helps identify the number of significant figures.

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