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Chapter: 11th 12th std standard Class Physics sciense Higher secondary school College Notes

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Measurement: Rounding off

Calculators are widely used now'a'days to do the calculations. The result given by a calculator has too many figures. In no case the result should have more significant figures than the figures involved in the data used for calculation.

Rounding off

 

Calculators are widely used now'a'days to do the calculations. The result given by a calculator has too many figures. In no case the result should have more significant figures than the figures involved in the data used for calculation. The result of calculation with number containing more than one uncertain digit, should be rounded off. The technique of rounding off is followed in applied areas of science.

 

A number 1.876 rounded off to three significant digits is 1.88 while the number 1.872 would be 1.87. The rule is that if the insignificant digit (underlined) is more than 5, the preceeding digit is raised by 1, and is left unchanged if the former is less than 5.

 

If the number is 2.845, the insignificant digit is 5. In this case, the convention is that if the preceeding digit is even, the insignificant digit is simply dropped and, if it is odd, the preceeding digit is raised by 1. Following this, 2.845 is rounded off to 2.84 where as 2.815 is rounded off to 2.82.


Examples

 

1. Add 17.35 kg, 25.8 kg and 9.423 kg.

 

Of the three measurements given, 25.8 kg is the least accurately known.

 

 17.35 + 25.8 + 9.423 = 52.573 kg

 

Correct to three significant figures, 52.573 kg is written as N     kg

 

2.   Multiply 3.8 and 0.125 with due regard to significant figures.

 

         3.8 x 0.125 = 0.475

 

The least number of significant figure in the given quantities is 2. Therefore the result should have only two significant figures.

 

         3.8 x 0.125 = 0.475 = 0.48


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