Q 2.10: 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 \ Nm^{-2}

(f) 0.0006032 \ m^{2}

Answers (1)
S safeer

(a) The given value is 0.007 \ m^2.

Since, the number is less than 1, the zeros on the right to the decimal before the first non-zero integer is insignificant. So, the number 7 is the only significant digit. 

\therefore It has 1 significant digit.

(b) The value is 2.64 \times 10^{24} kg

For the determination of significant values, we do not consider the power of 10 (Number is not less than 1). The digits 2, 6, and 4 are significant figures.

\therefore It has 3 significant digits.

(c)The value is 0.2370 \ g cm^{-3}.

For the given value with decimals, all the numbers 2, 3, 7 and 0 are significant.

\therefore It has 4 significant digits.

(d) The value is 6.320 \ J.

It has 4 significant digits.

(e)  The value is 6.032 \ Nm^{-2}.

 All the four digits are significant as the zeros in between two non-zero values are also significant. 

\therefore It has 4 significant digits.

(f) The value is 0.0006032 \ m^{2}

Same as (a), first three zeroes after the decimal is insignificant. Only 6, 0, 3, 2 are significant.

\therefore It has 4 significant digits.

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