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Question: State the number of significant figures in the following: a) \(0.007 m^2\) b) \(2.64 \times 10^{...

State the number of significant figures in the following:
a) 0.007m20.007 m^2
b) 2.64×10242.64 \times 10^{24} kg
c) 0.2370gcm−30.2370 g{cm^{-3}}
d) 6.320J6.320 J
e) 6.032Nm−26.032 N{m^{-2}}
f) 0.0006032m20.0006032m^2

Explanation

Solution

In measurement, the degree of correctness of a value compared to the original value is known as the accuracy of the measurement. Higher, the accuracy the smaller will be the difference between measured and original value. Number of digits in a value which contribute to the level of accuracy are termed as significant figures or digits.

Complete step by step answer:
a) 0.007m20.007 m^2 : In this case the number 0.007 can be written as 7×10−37 \times 10^{-3}. Hence, the only significant figure here is 7 i.e. there is only one significant figure in this number.

b) 2.64×10242.64 \times 10^{24} kg : In this case the number 2.64 has three figures which are non-zero figures, which makes all of them to be significant numbers. i.e. there are 3 significant figures in this case.

c) 0.2370gcm−30.2370 g{cm^{-3}} : Here, the number 0.2370 has three non-zero digits and one zero to the right of the decimal point, which follows the 3 non-zero digits. Hence, here we have four significant digits.

d) 6.320J6.320 J : Here, just like the previous case we have one such zero that follows non-zero numbers and lies to the right of the decimal point. So, three non-zero figures and one significant zero makes the total count of significant figures to be 4.

e) 6.032Nm−26.032 N{m^{-2}} : The number 6.032 can be written as 6032×10−36032 \times {10^{-3}}, we know that all non-zero digits are significant and a zero that lies between two significant digits is also a significant figure. Hence, here we have 4 significant figures.

f) 0.0006032m20.0006032m^2 : The given number can be written as 6032×10−76032 \times {10^{-7}}, hence, similar to the above case the total number of significant figures is 4.

Note: Rules for counting the significant numbers are given below. There are three rules on determining how many significant figures are in a number:

  1. Non-zero digits are always significant.
  2. Any zeros between two significant digits are significant.
  3. A final zero or trailing zeros in the decimal portion only are significant.