MATHEMATICS FORM 1 – APPROXIMATIONS

Is the process of rounding off a number in the given places in rounding makes numbers easier to deal with but at the same time reduces their accuracy.

The methods used for approximation or rounding off numbers are decimal places and significant figures.

ROUNDING OFF PROCEDURES

i) If the first neglected digit is greater or equal to 5 the digit occupying the place value will increase by 1 unit

ii) If the first neglected number is less than five, then the number occupying the required place value will remain unchanged.

ROUNDING OFF NUMBERS

Examples

1. Round off the following numbers to the nearest whole number.

a) 3425

b) 7.283

c) 6.674

d) 0.625

e) 36.12

f) 5446

Solutions

a) 3425≈ 3000

b) 7.283≈7

c) 6.674≈7

d) 0.625≈1

e) 36.12≈36

f) 5446≈5000

2. Round off the following to

a) 1 decimal place.

b) 2 decimal places.

c) 3 decimal places.

i) 23.7016

ii) 0.0094

Solution

i) 23.7016

1. 23.7016≈23.7 to 1 decimal place.
2. 23.7016≈23.70 to 2 decimal place.
3. 23.7016≈23.702 to 3 decimal places.

b) 0.0094

a) 0.0094≈0.0 to 1 decimal place.

b) 0.0094≈0.001 to 2 decimal place.

c) 0.0094≈0.009 to 3 decimal places.

3. Round off the following number to the nearest

a) Whole number

b) Tenth

c) Hundredth

i. 0.625

ii. 8.385

Solution

i. 0.625

a) 0.625≈1 to whole numbers

b) 0.625≈0.6 to tenth

c) 0.625≈0.63 to hundredths

ii. 8.385

a) 8.385≈8 to whole numbers

b) 8.385≈8.4 to tenth

c) 8.385≈ 8.39 to hundredths

Example: Round off 84678 to

i) Tens

Solution

84678 = 84700

ii) Hundreds

Solution

84678 = 85000

iii) Thousands

Solution

84678 = 80000

Example: Round off 179999 correct to i) hundreds ii) Thousand iii) Tens iv )Ten thousands

Solution

i) 179999180000

ii) 180000

iii) 180000

iv) 180000

Significant Figures
The are the total number of digits in the given number including zero’s which are in between non-zero digits.
Note

i) Zero is a significant figure when is in between two non – zero digits

ii) When zero is an outcome of approximation (rounding off) where a 9 receives l and becomes ten, then zero of ten is a significant figure.

Examples: determine the number of significant figures in the following

i) 20896100

= There are six significant figures

ii) 0.00025060

= There are four significant figures

iii) 2.00008453

= There are nine significant figures

Examples: Re write following numbers correcting to the required of significant figures.

a. 0.23678 to 3 significant figures

Solution

0.23678

∴= 0.24

b. 2.09478 to 3 significant figures

Solution

2.09478

∴= 2.09

c. 0.009994 to 2 significant figures

Solution

0.009994

∴= 0.010

d. 0.00931225697 to 7significant figures

Solutions

0.00931225697

∴= 0.0093123

Exercise

Re write the following numbers correctly to

a. 10.999009 to three significant figures

Solution

10.999009

∴= 11.0

b. 705.4005 to six significant figures

Solution

705.4005

= 705.401

C. 847910 to three significant figures

Solution

847910

∴= 848000

Approximations in operations

When you want to check approximation whether a calculation is correct or not. Round each number in the calculation to 1 significant figure. Do the calculation mentally.
Example:
A group of 42 people go to the cinema, which cost 680/- each. What is the approximation total cost?
Solution
Round 42 to 40 and 680 to 700
Therefore 40 x 700 = 28,000/=
Note: The exact cost is 28,560 The approximation is 28,000 which is close.