Question

(i)State the number of significant figures in the following:
(a)$0.007m^2$

(ii)State the number of significant figures in the following:
(b) $2.64\times {10}^{24}kg$

(iii)State the number of significant figures in the following:
(c) $0.2370gc{m}^{-3}$

(iv)State the number of significant figures in the following:
(d) $6.320J$

(v)State the number of significant figures in the following:
(e) $6.032N{m}^2$

(vi)State the number of significant figures in the following:
(f) $0.0006032m^2$

Answer 1

(i) Given : $0.007m^2$

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.

$\therefore 0.007m^2$ has one significant figure which is $7$

(ii) Given : $2.64\times {10}^{24}kg$

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

(iii) Given : $0.2370gc{m}^{-3}$

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

(iv) Given: $6.320J$

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

(v) Given :$6.032N{m}^2$
All zeroes between two non-zero digits are always significant.
$\therefore 6,0,3$ and $2$ are significant figures.

(vi) Given: $0.0006032m^2$
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 $(6,0,3,2)$ are significant