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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

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Answer Text

Solution :
(a) Answer: 1 <br> The given quantity is `0.007 m^2`. <br> 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. <br> Answer : 3 <br> The given quantity is `2.64 × 10^(24) kg`. <br> 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. <br> (c) Answer : 4 <br> The given quantity is `0.2370 g cm–3`.<br> 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. <br> (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.

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