#### Approximations and Estimations

- To round off a number means to find an approximate value. To approximate means to round off.
- When rounding off numbers, we round up or round down, depending on the digit to the right of the digit being rounded.
- If the digit to the right is 0, 1, 2, 3, 4, round down.
- If the digit to the right is 5, 6, 7, 8, 9, round up.

- Significant figures (s.f.) begin from the first non-zero digit at the left of a number. For example:
- 18329 to 2 s.f. = 18000
- 0.0092752 to 3 s.f. = 0.00928

- Decimal places (d.p.) are counted from the decimal point. Zeros after the point are taken into consideration. For example:
- 2.0816 to 1 d.p. = 2.1
- 2.0816 to 2 d.p. = 2.08
- 2.0816 to 3 d.p. = 2.082

__Examples__

__Examples__

- A football match is watched by 56742 persons. Write this number correct to the nearest,
- ten thousand
- 56742 to the nearest ten thousand = 60000

- thousand
- 56742 to the nearest thousand = 57000

- 10
- 56742 to the nearest ten = 56740

- ten thousand
- Write the following numbers correct to 3 sf:
- 47396
- 47396 to 3 sf = 47400

- 313179
- 313179 to 3 sf = 313000

- 20.294
- 20.294 to 3 sf = 20.3

- 0.0004678
- 0.0004678 to 3 sf = 0.000468

- 47396
- Write each of the following numbers correct to the number of decimal places specified.
- 0.2348 to 2 dp
- 0.2348 to 2 dp = 0.23

- 5.3989 to 3 dp
- 5.3989 to 3 dp = 5.399

- 124.5489 to 1 dp
- 124.5489 to 1 dp = 124.5

- 0.0008764 to 4 dp
- 0.0007764 to 4 dp = 0.0008

- 0.2348 to 2 dp
- Approximate 79.75 to the nearest
- hundred
- 79.75 to the nearest hundred = 100

- ten
- 79.75 to the nearest ten = 80

- whole number
- 79.75 to the nearest whole number = 80.
**NOTE**: The fraction 0.75 is nearer to 1 than 0; thus 79 is rounded up to the nearest whole number, 80)

- tenth
- 79.75 to the nearest tenth = 79.8
**NOTE**: The last digit of 79.75 is 5; round up

- hundred