Rounding Off
Calculators are widely used now-a-days to do calculations. The result given by a calculator has too many figures. In no case should the result have more significant figures than the figures involved in the data used for calculation. The result of calculation with numbers containing more than one uncertain digit should be rounded off. The rules for rounding off are shown in Table 1.10.
EXAMPLE 1.11
Round off the following numbers as indicated
i) 18.35 up to 3 digits
ii) 19.45 up to 3 digits
iii) 101.55 × 106 up to 4 digits
iv) 248337 up to digits 3 digits
v) 12.653 up to 3 digits.
Table 1.9 Rules for counting significant fig
| Rule | Example |
|---|---|
| i) All non-zero digits are significant | 1342 has four significant figures |
| ii) All zeros between two non zero digits are significant | 2008 has four significant figures |
| iii) All zeros to the right of a non-zero digit b to the left of a decimal point are significant | 30700 has five significant figures |
| iv) For the number without a decimal point, terminal or trailing zero(s) are not significant | 30700 has three significant figures |
| v) If the number is less than 1, the zero (s) o right of the decimal point but to left of the non zero digit are not significant. | 0.00345 has three significant figures |
| vi) All zeros to the right of a decimal point an to the right of non-zero digit are significant | 40.00 has four significant figures and 0.030400 has five significant figures |
| vii) The number of significant figures does no depend on the system of units used | 1.53 cm, 0.0153 m, 0.0000153 km, all have three significant figures |
Note 1: Multiplying or dividing factors, which are neith measured values, are exact and they have infinite numb example, circumference of circle S = 2πr, Here the facto 2.000 as required.
Note 2: The power of 10 is irrelevant to the determinat For example x = 5.70 m = 5.70 × \(10^2\) cm = 5.70 × \(10^3\) m In each case the number of significant figures is three.
Table 1.10 Rules for Rounding Off
| Rule | Example |
|---|---|
| i) If the digit to be dropped is smaller than 5,the preceding digit should be left unchanged | i) 7.32 is rounded off to 7.3 ii) 8.94 is rounded off to 8.9 |
| ii) If the digit to be dropped is greater than 5,the preceding digit should be increased by 1 | i) 17.26 is rounded off to 17.3 ii) 11.89 is rounded off to 11.9 |
| iii) If the digit to be dropped is 5 followed by digits other than zero, then the preceding digit sh be raised by 1 | i) 7.352, on being rounded off to first decimal becomes 7.4 ii) 18.159 on being rounded off to first decimal, become 18.2 |
| iv) If the digit to be dropped is 5 or 5 followe zeros, then the preceding digit is not chang it is even | i) 3.45 is rounded off to 3.4 ii) 8.250 is rounded off to 8.2 |
| v) If the digit to be dropped is 5 or 5 followe zeros, then the preceding digit is raised by is odd | i) 3.35 is rounded off to 3.4 ii) 8.350 is rounded off to 8.4 |
Solution
i) 18.4 ii) 19.4 iii) 101.6 × \(10^6\)
iv) 248000 v) 12.7