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Approximations

Significant Figures: The number of digits in a measurement about which we are certain plus one additional digit which is uncertain are known as significant figures.

 Thus, in 52.58 cm, there are four significant figures. Similarly, 10.434 have  5 significant digits.

Rules for Finding the Number of Significant Figures

Rule 1: All non-zero digits in a measurement are significant.

Example: -546.13  g has five significant figures. 307 m has three significant figures.

 Rule 2: In a decimal number which is greater than  1 , all digits (including zeros) are significant.

Example:

  • 205.002 kg has six significant figures.
  • 63.00 has four significant figures.
  • 2.50 has three significant figures
  • 92.0501 km has six significant figures

Rule 3: In a decimal number which lies between 0 and 1, all zeros to the right of the decimal point but to the left of the· first non-zero digit are not significant

Example: 0.00686   km has only  3   significant figures while  0.001010  kg has  4  significant figures.

Rule 4: If the measurement is a whole number, then the case becomes ambiguous if there are zeros to the left of an understood decimal point but to right of a non-zero digit.

Rule 5: All the final zeros in a decimal number obtained by rounding off a decimal to a given number of decimal places are significant.

Example: when  7.896  is rounded off to two decimal places, we get  7.90  , which has three significant figures

 

Rounding off a Decimal to the Required Number of Significant Figures

Sometimes during measurements it is required to obtain the value of a decimal number correct to the required number of significant figures.

Example: Round 74.312   kg to three significant figures:

Solution: The measurement  74.312   kg has  5   significant figures. To round it off to  3   significant figures, we are required to round it off to  1 place after the decimal. Therefore  74.312   kg =  74.3   kg rounded off to  3   significant figures.

 

Rounding off to a Specified Unit

Example: Round off: Rs.  64326   to the nearest  10   rupees. Rs.  64326 =   Rs.  64330   rounded to the nearest  10   rupees.

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