**APPROXIMATIONS**

CONTENT

- Revision of approximation.
- Accuracy of results using logarithm table and calculators.
- Percentage error.
- Application of approximation to every day life.

**REVISION OF APPROXIMATION**

An approximation helps us to see and understand easily the size of a number. It is a number taken as close as possible to the actual value of the number.

In order to come close to the actual value, the number must be rounded off. This implies digits 1 to 4 are rounded down while those from 5 to 9 are rounded up. Other methods could be approximating to decimal places or significant figures.

Decimal places mean the number of places after the decimal point while significant figure is the first non-zero digit from the left.

**Example 1:** The distance between the earth and the sun is \(148729440km\). Round this number to the nearest (a) million (b) 2 s.f (c) 3 s.f

**SOLUTION**

(a) \(148729440km = 149000000km\) (i.e round 7 up)

(b) \(148729440km = 150000000km\) (i.e round 8 up)

(c) \(148729440km = 149000000km \) (i.e round 7 up)

**EXAMPLE 2: **Write \(78.45831kg \) to (i) 2 d.p, (ii) 3 d.p

**SOLUTION **

(i) \(78.45831kg = 78.46kg\) (i.e round 8 up)

(ii) \(78.45831kg = 78.458kg\) (round down 3)

(b) Round \(0.0004996\) to (i) 1 s.f (ii) 2 s.f

**SOLUTION**

(i) \(0.0004996 = 0.0005\) (round the first 9 up)

(ii) \(0.0004996 = 0.00050\) (round the second 9 up)

**CLASS ACTIVITY**

- Round off \(586.5764\) to (i) 1 d.p (ii) 3 d.p
- Approximate \(964572183665\) to (i) 3 s.f (ii) 6 s.f

** **

**ACCURACY OF RESULTS USING LOGARITHM TABLE AND CALCULATORS**

All measurements are approximations, so they cannot be exact.

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