Question

State the number of significant figures in the following:

$\left(a\right)0.007m^2$

$\left(b\right)2.64\times {10}^{24}kg$

$\left(c\right)0.2370gc{m}^{-3}$

$\left(d\right)6.320J$

$\left(e\right)6.032N{m}^{-2}$

$\left(f\right)0.0006032m^2$

Answer 1

The significant figures of a number are those digits that carry meaning contributing to its measurement resolution. This includes all digits except:
1. All leading zeros;
2. Trailing zeros when they are merely placeholders to indicate the scale of the number (exact rules are explained at identifying significant figures);
3. Spurious digits introduced, for example, by calculations carried out to greater precision than that of the original data, or measurements reported to a greater precision than the equipment supports.
(a)

$0.007=$ $7\times {10}^{-3}$
Significant digit $=7$
Only one significant digit.

(b) Number of significant digit $=3$

(c)

All non-zero numbers are always significant.All zeroes before a non zero number are insignificant. All zeroes which are simultaneously to the right of the decimal point and at the end of the number are significant. The only non significant digit here is the zero before the decimal point.
Hence, number of significant digits is $4$.

(d)

All non-zero numbers are always significant. All zeroes which are simultaneously to the right of the decimal point and at the end of the number are significant.
Hence, number of significant digits is $4$.

(e)

All the digits are significant. (no leading and trailing zero)
No. of significant digits $=4$

(f)

Significant digits $=6032$
No. of sig. digits $=4$