Question

State the number of significant figures in the following :
(a) 0.007 m2 (b) 2.64 × 1024 kg (c) 0.2370 g cm–3 (d) 6.320 J (e) 6.032 N m–2 (f) 0.0006032 m2

Answer 1

(a) The given quantity is 0.007 m2: 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.

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(b) The given quantity is 2.64 × 1024 kg: Here, the power of 10 is irrelevant for the determination of significant figures. Hence, If the number is less than one, then all zeros on the right of the decimal point (but left to zero) are insignificant. This means that here, two zeros after the decimal are Here, the power of 10 is irrelevant for the determination of significant figures. Hence, all $\frac{9}{31}$ digits i.e., 2, 6 and 4 are significant figures.

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(c) The given quantity is 0.2370 g cm -3: For a number with decimals, the trailing zeroes are significant. Hence, besides digits 2, 3, and 7, 0 which appears after the decimal point is also a significant figure.

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(d) 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.

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(e) The given quantity is 6.032 J: Nm All zeroes between two non-zero digits are always significant.

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(f) The given quantity is 0.0006032 m: 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.