# APPROXIMATION OF NUMBERS ROUNDING

## APPROXIMATION OF NUMBERS ROUNDING OFF TO DECIMAL PLACES

Digits 1,2,34 are rounded down to Zero, while digits 5, 6, 7, 8, and 9 are rounded up to 1 e.g. 126=130 to 2 digits

A significant figure begins from the first non-zero digit at the left of a number. Digit should be written with their correct place values.

Worked example

1. Round off the following to the nearest
2. Thousand (ii) hundred (ii) ten

(a) 8615 (b) 16,560

Solution

a.

1. i) 8615 ≈ 9000 {to the nearest thousand}
2. ii) 8615 ≈8600 {to the nearest hundred}

iii) 8615 ≈8620 {to the nearest ten}

b.

(i) 16560≈17000 {to the nearest thousand}

(ii) 1660≈16, 600 {to the nearest hundred}

(iii) 16560 ≈16560 {to the nearest ten}

1. Round off the following to the nearest (i) whole number (ii) tenth (iii) hundred

(a) 3.125 (b) 0.493

Solution

a.

(I)   3.125≈3 {to the nearest whole number}

(ii)  3.125≈3.1{to the nearest tenth}

(iii) 3.125≈3.13{to the nearest hundredth}

b.

(i) 3.125≈3 {to the nearest whole number}

(ii) 3.125≈3.1{to the nearest tenth}

(iii) 3.125≈3.13{to the nearest hundredth

Evaluation

Round off the following to

1. a) p. (b) 2 d.p.   (c) 3 d.p.

(1) 12.9348  (2)  5.0725     (3)  0.9002

## Square Roots of Numbers

The symbol ‘√’ means “square root of”. To find the square root of a number, first find its factors.

Examples

1. Find the square root of 11025

Solution

(a) √11025

3                11025

3                3675

5                1225

5                   245

7                    49

7                       7

√11025= √(32 x 52 x 72)= 3 X 5 X 7=105

Example

Find the square roots of  √54/9

Solution:

√54/9 =√49/9=√49/√9=7/3=2 1/3

## WEEKEND ASSIGNMENT

1. What is 0.003867 to 3 significant figure (a)0.004 (b)0.00386 (c)0.00387 (d)386
2. The square root of 121/2 is ____(a)1 3/4 (b)3 1/2 (c)3 3/4 (d)6 1/4
3. 9852 to 3 S.F. is _____(a)990 (b) 9850 (c) 9580 (d) 986
4. 7.0354 to 2 d.p is _____(a) 7.03(b) 7.04 (c) 7.40 (d)7.13
5. 59094 to the nearest hundred is ____(a) 59100(b)59104 (c) 60094 (d) 60194

## THEORY

1. Find the square root of 1296
2.   a.  What is 0.046783 to 3 significant figure
3.   45.34672 to 2 d.p. is ______