State the number of significant figures in the following : (a) `0.007m^2` (b) `2.64 xx10^(24) kg` (c ) `0.2370 g cm^(-3)` (d) `6.320 J` (e ) `6.032 N m^(-2)` (f) `0.0006032 m^2`

Explanation

(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.
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.