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
(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
Solution and Explanation
(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.
(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.
(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.
(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.
(e) The given quantity is 6.032 J: Nm All zeroes between two non-zero digits are always significant.
(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.
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Concepts Used:
Significant Figures
The significant figures of a given number are those significant or important digits, which convey the meaning according to its accuracy. For example, 6.658 has four significant digits. These substantial figures provide precision to the numbers. They are also termed as significant digits.
Rules for Significant Figures:
- All non-zero digits are significant. 198745 contains six significant digits.
- All zeros that occur between any two non zero digits are significant. For example, 108.0097 contains seven significant digits.
- All zeros that are on the right of a decimal point and also to the left of a non-zero digit is never significant. For example, 0.00798 contained three significant digits.
- All zeros that are on the right of a decimal point are significant, only if, a non-zero digit does not follow them. For example, 20.00 contains four significant digits.
- All the zeros that are on the right of the last non-zero digit, after the decimal point, are significant. For example, 0.0079800 contains five significant digits.
- All the zeros that are on the right of the last non-zero digit are significant if they come from a measurement. For example, 1090 m contains four significant digits.