Approximation of Numbers Rounding off to Decimal Places, Significant Figures

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In today’s Mathematics class, We will be discussing “Approximation of Numbers”. We hope you enjoy the class!

 

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 (i) Thousand (ii) hundred (ii) ten

(a) 8615 (b) 16,560

Solution

a.

1. 1. 1. 1. i) 8615 ≈ 9000 {to the nearest thousand}
         2. ii) 8615 ≈8600 {to the nearest hundred}
         3. 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}

 

2. 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) 0.493≈0 {to the nearest whole number}

(ii) 0.493≈0.5{to the nearest tenth}

(iii) 0.493≈0.49{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

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  √49/9 

Solution:

$\sqrt{\raisebox{1ex}{$49$}\!\left/ \!\raisebox{-1ex}{$9$}\right.} = \frac{\sqrt{49}}{\sqrt{9}} = \frac{7}{3} = 2\frac{1}{3}$

 

 

READING ASSIGNMENT

New General Mathematics, UBE Edition, Chapter 2, pages 28-32, 20-21

Essential Mathematics by A J S Oluwasanmi, Chapter 1, pages 42-45

 

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. b. 45.34672 to 2 d.p. is ______

 

 

We have come to the end of this class. We do hope you enjoyed the class?

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In our next class, we will be talking about Multiplication and Direction of Directed and Non-directed numbers. We are very much eager to meet you there.

 

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