Lesson 8, Topic 1
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# Significant Figures (S.F)

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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.

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.

### Example 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

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

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

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

### Example 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

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

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

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

### Example 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

#### Responses error: