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Properties of Whole Numbers I | Week 14 Topics1 Quiz
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Properties of Whole Numbers II | Week 24 Topics1 Quiz
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Properties of Whole Numbers III | Week 35 Topics1 Quiz
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Indices | Week 42 Topics1 Quiz
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Laws of Indices | Week 55 Topics1 Quiz
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Whole Numbers & Decimal Numbers | Week 64 Topics1 Quiz
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Standard Form | Week 73 Topics1 Quiz
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Significant Figures (S.F) | Week 84 Topics1 Quiz
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Fractions, Ratios, Proportions & Percentages I | Week 96 Topics1 Quiz
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Fractions, Ratios, Proportions & Percentages II | Week 104 Topics1 Quiz
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Fractions, Ratios, Proportions & Percentages III | Week 113 Topics1 Quiz
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Approximation & Estimation | Week 121 Topic1 Quiz
Topic Content:
- Significant Figures (S.F)
Significant figures are non-zero digits but that does not mean that zeroes are not significant. The zeroes in between significant digits are also significant. The first non-zero significant figure as you read a number from left is the first significant figure e.g.
| 1st S.f | 2nd S.f | 3rd S.f | 4th S.f | 5th S.f | 6th S.f | 7th S.f | 8th S.f |
| 2 | 5 | 6 | 7 | 0 | 0 | 5 | 2 |
| 1st S.f | 2nd S.f | 3rd S.f | 4th S.f | |||||
| 0 | . | 0 | 0 | 0 | 1 | 2 | 3 | 4 |
Significant figures show the precision of an answer. When a television newscaster reports that a man has won a ₦2 Million lottery, this has been rounded up to one Significant figure. It rounds to the most important figure in the number.
Rounding to Significant Figures:
The method of rounding to a significant figure is the same for either big or small numbers. The first significant figure is the first non-zero digit as you read a number from the left.
Steps:
1. Look for the required significant figure digit
2. Draw a vertical line after the place value digit that is required.
3. Look at the next digit
4. If it is 5 or more, increase the previous digit by 1
5. If it is 4 or less, the previous digit remains the same.
6. Fill any spaces to the right of the line with zero, stopping at the decimal/point if there is any.
Worked Example 8.1.1:
Round the following numbers correct to (a) 1 s.f (b) 2 s.f (c) 3 s.f
i. 3762
ii. 18.05
iii. 0.0006081
Solution i
a. 3 | 762
| 1st S.f | 2nd S.f | 3rd S.f | 4th S.f |
| 3 | 7 | 6 | 2 |
7 is closest to 3 (1st s.f)
7 is a round-up number so we add 1 to 3 which gives 4.
= 4000 to 1 s.f
b. 37|62 = 3800 to 2s.f
| 1st S.f | 2nd S.f | 3rd S.f | 4th S.f |
| 3 | 7 | 6 | 2 |
6 is closest to 7 (2nd s.f)
6 is a round-up number so we add 1 to 7 which gives 8.
= 3800 to 2 s.f
c. 376 | 2 = 3760 to 3 s.f
| 1st S.f | 2nd S.f | 3rd S.f | 4th S.f |
| 3 | 7 | 6 | 2 |
2 is closest to 6 (3rd s.f)
2 is a round-down number so we add 0
= 3760
Solution ii
a. 1|8.05 = 20 to 1 s.f
b. 18|.05 = 18 to 2 s.f
c. 18.0 |5 = 18.1 to 3 s.f
Solution iii
a. 0.0006 | 081 =0.0006 to 1 s.f
b. 0.00060 | 81 = 0.00061 to 2 s.f
c. 0.000608 | 1 = 0.000608 to 3 s.f
Worked Example 8.1.2:
Give the following, correct to
i. 1 s.f
ii. 2 s.f
iii. 3 s.f
iv. 4 s.f
a. 6853
b. 29.56785
Solution a
i. 6853 to 1 s.f
| 1st S.f | 2nd S.f | 3rd S.f | 4th S.f |
| 6 | 8 | 5 | 3 |
8 is closest to 6 (1st s.f)
8 is a round-up number so we add 1 to 6.
Every other digit after the significant digit becomes zero.
= 7000 to 1 s.f
ii. 6853 to 2 s.f
| 1st S.f | 2nd S.f | 3rd S.f | 4th S.f |
| 6 | 8 | 5 | 3 |
5 is closest to 8 (2nd s.f)
5 is a round-up number so we add 1 to 8.
Every other digit after the significant digit becomes zero.
= 6900 to 2 s.f
iii. 6853 to 3 s.f
| 1st S.f | 2nd S.f | 3rd S.f | 4th S.f |
| 6 | 8 | 5 | 3 |
3 is a round-up number so we add 0
= 6850 to 3 s.f
Solution b
i. 29.56785 to 1 s.f
= 30 to 1 s.f
ii. 29.56785 to 2 s.f
= 30 to 2 s.f
iii. 29.56785 to 3 s.f
= 29.6 to 3 s.f
Worked Example 8.1.3:
Give 0.006098 to
i. 1 s.f
ii. 2 s.f
iii. 3 s.f
Solution
i. 0.006098 to 1 s.f
= 0.006 to 1 s.f
ii. 0.006098 to 2 s.f
= 0.0061 to 2 s.f
iii. 0.006098 to 3 s.f
= 0.00610 to 3 s.f