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

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

(a) 8615 (b) 16,560

Solution

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

iii) 8615 ≈8620 {to the nearest ten}

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

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

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

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

(a) 3.125 (b) 0.493

Solution

(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}

(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

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

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

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

THEORY

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