 |
| Introduction |
|
| We use specific number of digits to denote an exact value of a number for required accuracy. The digits used for such a purpose are called significant figures. |
| |
| Suppose a measurement is recorded as 0.6204 cm. It means that the measurement was made correct to the nearest 0.0001 cm. There are 6204 of 0.0001 cm units of measurement. The number of significant figures is four. The figures are 6, 2, 0 and 4. |
| |
| Consider the following examples: |
| |
| (i) The height of a tower is 158.6 m. Its value is accurate to four significant figures. |
| |
| (ii) If it is written as approximately 159 m, it is accurate to three significant figures. The height is rounded to the nearest
meter. |
| |
| (iii) If it is written as approximately 160 m, it is accurate to two significant figures. The 0 in the units place is not significant because it is used only to show that the height is rounded to the nearest 10 m. |
| |
| (iv) Mr. X is 109 cm tall. The unit of accuracy required is
centimeters. |
| |
| Therefore, all the three digits are significant. |
| |
| (v) The thickness of a metal wire is 0.02 cm. The unit of accuracy required is hundredth of a centimeter. |
| |
| Therefore, only digit 2 is significant. |
| |
| The 0 after decimal indicates the magnitude of measurement. Therefore, the 0 after decimal point is not significant. .02 cm has one significant figure. |
| |
| To sum up the above examples: |
| |
| (a) For a number between 0 and 1, the successive zeros after decimal are not significant. |
| |
| Each of the numbers 0.092, 0.0037, 0.00089 has two significant figures. |
| |
| (b) For a number with a decimal point, the final zeros are significant. Each of the numbers 47.00, 4.700, 0.4700 has four significant figures. |
| |
| (c) For a number beginning and ending with non-zero digits, all digits are significant. |
| |
| Each of the numbers 4207, 402.7, 4.075, 0.4007 has four significant figures. |
| |
| (d) For a whole number, the final zeros are not significant, unless the accuracy demanded states so. |
| |
| Each of the numbers 4320, 59300, 987000 has three significant figures. |
| |
