Second Term Lesson Note for Week Two
Class : JSS 1
Subject : Mathematics
Topic : Approximation
Duration : 80 Minutes
Period : Double Periods
Reference Book :
- Essential Mathematics for Junior Secondary Schools, JSS 1.
- Lagos State Unified schemes of work for Junior Secondary Schools, (JSS 1 – 3).
- Online Resources
Instructional Material : Chart showing the basic rules applied in approximation of numbers.
Learning Objectives : By the end of the lesson learners will be able to :
i. Explain the meaning of Approximation.
ii. Identify the forms of approximation of numbers, with
iii. Solve several examples on approximation of numbers.
Content :
APPROXIMATION
Approximation is the process of using rounded numbers, to estimate the outcome of calculations.
Approximation can help us decide whether an answer to a calculation is right or not. We can approximate numbers by rounding them up to decimal places, significant figures, nearest whole number, tens , hundreds etc.
A.) Decimal Place/Point :
A number such as 197.7658 is an example of a decimal number. The whole number part is 197 and the decimal part is 7658. The point between them is called a decimal point.
197.7658
Whole number. Decimal
Decimal point
To find the number of decimal places (d.p) simply count the number of figures after the decimal point. Thus, the number above has 4 d.p.
197.7658
4th decimal place
3rd decimal place
2nd decimal place
1st decimal place
Guidelines to rounding off numbers:
To round off numbers to a specific number of decimal places (d.p)
1. Look for the last digit (i.e. the required decimal place you are rounding to)
2. Then look at the next digit to the right, i.e. the decider
3. If the decider is 5 or more round up (i.e. add 1 to the last digit) if it is less than 5, then add nothing.
Examples : Give the number 78.05624 correct to (a) 1 d.p (b) 2 dp (c) 3 dp
Solution :
78.1 (start counting from the number after the point. Note that zero is significant).
78.06 (after counting the number check the next number, if the number is less than 5 or <; it changes to zero but if it is 5 or > it changes to 1 and then add to the next counted before it.)
78.056 (since the number is less it turns to zero and it has no significance)
Example 2:
Give 57.9945 correct to (a) 2dp (b) 4dp
Solution :
(a) 57.9945 = 57.99 (to 2 d.p.)
(b) 57.9945 = 57.9945 (to 4 d.p.)
B.) Significant Figure :
The word significant means ‘important or non zero digits’ and it is another way of approximating numbers. We write significant figure as (S.f.).
Numbers greater than zero
For example, the number 865 034 has six figures or digits. The first figure from the left i.e. 8 is worth 800 000 (place value) and it is the most significant figure. It is therefore the first significant figure and 4 the least or sixth significant figure.
Also in the number : 987634
9 is the 1st s.f. = 1000 000 ( to 1 s.f.)
8 is the 2nd s.f. = 990000 ( to 2 s.f)
7 is the 3rd s.f. = 988000 (to 3 s.f.)
6 is the 4th s.f. = 987600 ( to 4 s.f.)
3 is the 5th s.f. = 987630 ( to 5 s.f.)
4 is the 6th s.f. = 987634 ( to 6 s.f.)
Numbers less than zero
For example 0.000007685 is given to 8 decimal places.
The first zero before the decimal number means that the zero is units, and the 5 zeros after the decimal point mean that they are insignificant figures. Therefore, the most significant number or first significant figure in 0.000007682 is 7 follow by 6 and 8.
0. 0 0 0 0 0 7 6 8 2
7 is the 1st s.f. = 0.000008 to 1 s. f.
6 is the 2nd s.f. = 0.0000077 to 2 s. f.
8 is the 3rd s.f. = 0.00000768 to 3 s. f.
Note: the first significant figure is always the first non-zero figure as you read the number from the left hand side to your right hand side.
Guide to round off numbers :
To correct a number to a specific number of significant figure
i. Look for the required significant figure
ii. Look at the next significant figure to the right (i.e. the decider)
If the decider is 5 or more round up to 1 and add it to the number but if it is less than 5, round it down to zero and add zero to the number that precedes or comes before it.
For Example :
1. Given 4540 correct to (a) 1 s.f. (b) 2 s. f. (c) 3 s.f.
Solution :
Note the figures above, it helps just follow the figure correctly.
a.) 4540 = 5000 (the reason for getting 5000 after Selecting 4, the next number is 5 which will turn to 1 and add to the 4 counted and the other numbers turn to zeros).
b.) 4540 = 4500 (after counting 2 s.f the next number is 4 which turn to zero and add to 5 to be 6 and the rest turn to zeros.
c. ) 4540 = 4540 (after counting 3 s.f. the next number is a zero, which then give rise to the same number).
Example 2 : Convert 0.0000579 to (a) 2 s.f. (b) 3 s.f. (c) 1 s.f.
Solution :
(a) 0.0000579 = 0.000058 (to 2 s.f.)
(b) 0.0000579 = 0.0000579 (to 3 s.f.)
(c) 0.0000579 = 0.00006 (to 1 s.f.)
2.3 Rounding Decimals to the Nearest, Tenth, Hundredth, and Thousandths and Whole.
Example 3 :
Give 474.4547 correct to the nearest
a. Tenth
b. Hundredth0.0000579
c. Thousandth
Solution :
Note: that the counting starts after the point.
i. 474.4547 = 474.5 (since the next number after counting is 5/>, it turns to 1 and added to the counted 4 to give 5)
ii. 474.4547 = 474.45 ( to the nearest hundredth)
iii. 474.4547 = 474.455 (to the nearest thousandth)
Example 4 : Round off
(a) 13.73
(b) 34.245 (to the nearest whole number) .
Solution :
a.) 13.73 = 14 (since the whole is 13 the next number is decimal which is 7, it is rounded up to 1 and added to 13 to give 14).
b.) 34.245 = 34 (since the whole number is 34 and next number that follows is 2, that is less than 5. Hence, the 2 is rounded down to zero and added to give us 34).
ASSIGNMENT :
ESSENTIAL MATHEMATICS BOOK 1
EXERCISE 8.5 page 89 No. 2(a,b,c,d), 5+ (a,b,c)