## 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. $$\therefore 24.68=20\,(1\text{ s.f})$$