Round off a number to certain numbers of significant figures

Significant Figures

2.1

Significant Figures

	Definition

	Significant figure shows the level of accuracy of a measurement.

All digits are significant figures except the zero before the first non-zero digit.

	Example

	(i)		\(0.032\rightarrow 2\text{ s.f.}\)

	(ii)		\(0.0740\rightarrow 3\text{ s.f.}\)

Integers:

The value of significant figure for zero as the last digit depends on the required level of accuracy.

	Example

	(i)		\(24\,000 \rightarrow 5\text{ s.f.}\) (if the level of accuracy is to the nearest one)

	(ii)		\(24\,000 \rightarrow 2\text{ s.f.}\) (if the level of accuracy is to the nearest thousand)

	(iii)		\(24\,000 \rightarrow 3\text{ s.f.}\) (if the level of accuracy is to the nearest hundred)

Round of significant figures:

For integers, the decimal point is placed behind the last digit.
The first non-zero digit is a significant figure.
The digits before the decimal point will be placed with \(0\) when rounding off.

	Example

	(i)		Round off \(7\,861\) to \(2\) significant figures.

			The digit to be rounded off is \(8\). \(6 \gt 5\), thus add \(1\) to \(8\). \(6 \) and \(1\) are placed before decimal point. Thus, replace \(6 \) and \(1\) with \(0\). \(\therefore 7\,861=7\,900\,(2\text{ s.f})\)

	(ii)		Round off \(8\,213\) to \(3\) significant figures.

			The digit to be rounded off is \(1\). \(3\lt 5\), thus digit \(1\) remains unchanged. \(3\) is placed before decimal point. Thus, replace \(3\) with \(0\). \(\therefore 8\,213=8\,210\,(3\text{ s.f})\)

	(iii)		Round off \(24.68\) to \(1\) significant figure.

			The digit to be rounded off is \(2\). \(4\lt 5\), thus digit \(2\) remains unchanged. \(4\) is placed before decimal point. Thus, replace \(4\) with \(0\). \(6\) and \(8\) are dropped. \(\therefore 24.68=20\,(1\text{ s.f})\)

Significant Figures

2.1

Significant Figures

	Definition

	Significant figure shows the level of accuracy of a measurement.

All digits are significant figures except the zero before the first non-zero digit.

	Example

	(i)		\(0.032\rightarrow 2\text{ s.f.}\)

	(ii)		\(0.0740\rightarrow 3\text{ s.f.}\)

Integers:

The value of significant figure for zero as the last digit depends on the required level of accuracy.

	Example

	(i)		\(24\,000 \rightarrow 5\text{ s.f.}\) (if the level of accuracy is to the nearest one)

	(ii)		\(24\,000 \rightarrow 2\text{ s.f.}\) (if the level of accuracy is to the nearest thousand)

	(iii)		\(24\,000 \rightarrow 3\text{ s.f.}\) (if the level of accuracy is to the nearest hundred)

Round of significant figures:

For integers, the decimal point is placed behind the last digit.
The first non-zero digit is a significant figure.
The digits before the decimal point will be placed with \(0\) when rounding off.

	Example

	(i)		Round off \(7\,861\) to \(2\) significant figures.

			The digit to be rounded off is \(8\). \(6 \gt 5\), thus add \(1\) to \(8\). \(6 \) and \(1\) are placed before decimal point. Thus, replace \(6 \) and \(1\) with \(0\). \(\therefore 7\,861=7\,900\,(2\text{ s.f})\)

	(ii)		Round off \(8\,213\) to \(3\) significant figures.

			The digit to be rounded off is \(1\). \(3\lt 5\), thus digit \(1\) remains unchanged. \(3\) is placed before decimal point. Thus, replace \(3\) with \(0\). \(\therefore 8\,213=8\,210\,(3\text{ s.f})\)

	(iii)		Round off \(24.68\) to \(1\) significant figure.

			The digit to be rounded off is \(2\). \(4\lt 5\), thus digit \(2\) remains unchanged. \(4\) is placed before decimal point. Thus, replace \(4\) with \(0\). \(6\) and \(8\) are dropped. \(\therefore 24.68=20\,(1\text{ s.f})\)