State the number of significant figures in the following:
$(a)$ $0.007 \;m^{2}$
$(b)$ $2.64 \times 10^{24} \;kg$
$(c)$ $0.2370 \;g \;cm^{-3}$
$(d)$ $6.320 \;J$
$(e)$ $6.032 \;N \;m^{-2}$
$(f)$ $0.0006032 \;m^{2}$

(N/A) The given quantity is $0.007 \;m^{2}$.
If the number is less than $1$,the zeros on the right of the decimal point but to the left of the first non-zero digit are not significant. Thus,only $7$ is significant. Number of significant figures = $1$.
$(b)$ The given quantity is $2.64 \times 10^{24} \;kg$.
The power of $10$ does not affect the number of significant figures. The digits $2, 6, 4$ are significant. Number of significant figures = $3$.
$(c)$ The given quantity is $0.2370 \;g \;cm^{-3}$.
In a number with a decimal,trailing zeros are significant. Thus,$2, 3, 7, 0$ are significant. Number of significant figures = $4$.
$(d)$ The given quantity is $6.320 \;J$.
Trailing zeros in a number with a decimal are significant. Thus,$6, 3, 2, 0$ are significant. Number of significant figures = $4$.
$(e)$ The given quantity is $6.032 \;N \;m^{-2}$.
Zeros between two non-zero digits are always significant. Thus,$6, 0, 3, 2$ are significant. Number of significant figures = $4$.
$(f)$ The given quantity is $0.0006032 \;m^{2}$.
Zeros to the right of the decimal point but to the left of the first non-zero digit are not significant. The digits $6, 0, 3, 2$ are significant. Number of significant figures = $4$.