Question

The diameter of a sphere is measured as 1.93 cm. If the measuring instrument has a least count of 0.01 cm, the radius to correct significant figures and after rounding off will be -

1. 0.965 cm
2. 0.96 cm
3. 0.9 cm
4. 0.9650 cm

Answer 1

Correct Answer - Option 2 : 0.96 cm

The correct answer is option 2) i.e. 0.96 cm

CONCEPT:

• Significant figures are numbers that add to the precision of the overall value of the number.
  • ​The reliable digits plus the first uncertain digit are known as significant digits or significant figures.
  • ​For example, 23.4 has 2 and 3 as reliable digits and the digit 4 is uncertain.
• ​Rounding off the uncertain digits: The result of computation with approximate numbers, which contain more than one uncertain digit, should be rounded off. The rules for rounding off numbers to the appropriate significant figures are:
  • The preceding digit is raised by 1 if the insignificant digit to be dropped is more than 5, and is left unchanged if the latter is less than 5.
  • When the insignificant digit is 5: if the preceding digit is even, the insignificant digit is simply dropped and, if it is odd, the preceding digit is raised by 1.
• Rules for arithmetic operations with significant figures:
  1. ​​In multiplication or division, the final result should retain as many significant figures as are there in the original number with the least significant figures.
  2. In addition or subtraction, the final result should retain as many decimal places as are there in the number with the least decimal places.

EXPLANATION:

Diameter = radius ÷ 2 = 1.93 ÷ 2 = 0.965 cm

• Here the least count is 0.01 cm.
• So the number of significant figures required in the result is two.
• 0.965 cm can be rounded off to 0.96 cm in two significant figures.
• Thus, the correct value of radius is 0.96 cm.

​

• The rules to be followed in determining or representing significant figures are as listed:
  1. All non-zero numbers are significant.
  2. Zeros between two non-zero digits are significant.
  3. Trailing zeros to the right of the decimal is significant.
  4. Trailing zeros in a whole number with the decimal shown is significant.
  5. Trailing zeros in a whole number with no decimal shown is not significant.
  6. A choice of change of different units does not change the number of significant digits or figures in a measurement