__Question 2.10__:

State the number of significant figures in the following :

(a) 0.007 m

^{2}

(b) 2.64 10

^{24}kg

(c) 0.2370 g cm–

^{-3}

(d) 6.320 J

(e) 6.032 N m–^{-2}

(f) 0.0006032 m

^{2}

^{}

__Solution__:

(a)

**Answer:**1

The given quantity is 0.007 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 × 10

^{24}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 g 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 N m

^{–2}.

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

(f)

**Answer:**4

The given quantity is 0.0006032 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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