The mass of a box measured by a grocer’s balance is 2.30 kg. Two gold pieces of masses 20.15 \(\text g\) and 20.17 \(\text g\) are added to the box. What is - the total mass of the box,
- the difference in the masses of the pieces to correct significant figures ?
- the total mass of the box,
- the difference in the masses of the pieces to correct significant figures ?
Solution and Explanation
a. Mass of grocer’s box = 2.300 \(\text {kg}\)
Mass of gold piece I = 20.15 \(\text g\) = 0.02015 \(\text {kg}\)
Mass of gold piece II = 20.17 \(\text g\) = 0.02017 \(\text {kg}\)
Total mass of the box = 2.3 + 0.02015 + 0.02017 = 2.34032 \(\text {kg}\)
In addition, the final result should retain as many decimal places as there are in the number with the least decimal places.
Hence, the total mass of the box is 2.3 \(\text {kg}\).
b. Difference in masses = 20.17 - 20.15 = 0.02 \(\text g\)
In subtraction, the final result should retain as many decimal places as there are in the number with the least decimal places.
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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.