State the number of significant figures in the following:
Question.
State the number of significant figures in the following:

(a) $0.007 \mathrm{~m}^{2}$

(b) $2.64 \times 10^{24} \mathrm{~kg}$

(c) $0.2370 \mathrm{~g} \mathrm{~cm}^{-3}$

(d) $6.320 \mathrm{~J}$

(e) $6.032 \mathrm{~N} \mathrm{~m}^{-2}$

(f) $0.0006032 \mathrm{~m}^{2}$

solution:

(a) Answer: 1

The given quantity is $0.007 \mathrm{~m}^{2}$.

If the number is less than one, then all zeros on the right of the decimal point (but left to the first non-zero) are insignificant. This means that here, two zeros after the decimal are not significant. Hence, only 7 is a significant figure in this quantity.

(b) Answer: 3

The given quantity is $2.64 \times 10^{24} \mathrm{~kg}$.

Here, the power of 10 is irrelevant for the determination of significant figures. Hence, all digits i.e., 2, 6 and 4 are significant figures.

(c) Answer: 4

The given quantity is $0.2370 \mathrm{~g} \mathrm{~cm}^{-3}$.

For a number with decimals, the trailing zeroes are significant. Hence, besides digits 2,3 and 7,0 that appears after the decimal point is also a significant figure.

(d) Answer: 4

The given quantity is 6.320 J.

For a number with decimals, the trailing zeroes are significant. Hence, all four digits appearing in the given quantity are significant figures.

(e) Answer: 4

The given quantity is $6.032 \mathrm{Nm}^{-2}$.

All zeroes between two non-zero digits are always significant.

(f) Answer: 4

The given quantity is $0.0006032 \mathrm{~m}^{2}$.

If the number is less than one, then the zeroes on the right of the decimal point (but left to the first non-zero) are insignificant. Hence, all three zeroes appearing before 6 are not significant figures. All zeros between two non-zero digits are always significant. Hence, the remaining four digits are significant figures.
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