Week 1 and 2 – Jss 1 Second Term Mathematics Lesson Notes

SUBJECT:
MATHEMATICS
CLASS:
JUNIOR SECONDARY SCHOOL 1
SCHEME OF WORK
WEEK 1        REVISION OF LAST WORK
WEEK 2        APPROXIMATION
WEEK 3        APPROXIMATION
WEEK 4        NUMBER BASE
WEEK 5        NUMBER BASE
WEEK 6        BASIC OPERATION
WEEK 7        REVIEW OF FIRST TERM
WEEK 8        BASIC OPERATION
WEEK 9        ALGEBRAIC PROCESS
WEEK 10        ALGEBRAIC PROCESS
WEEK 11        REVISION
WEEK 12        EXAMINATION
WEEK2:            APPROXIMATION
2.0    Introduction:
Approximation is the process of using rounded numbers, to estimate the outcome of calculations. Approximationcan 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.

 2.1    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

 Guide to round off numbers:
To round off numbers to a specific number of decimal places
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.

 Examples2.1: Give the number 78.05624 correct to (a) 1 d.p (b) 2 dp (c) 3 dp
Solution:

1. 78.1 (start counting from the number after the point. Note that zero is significant).
2. 78.06 (after counting the number check the next number, if the number is less than 5/<; it changes to zero but if it is 5 or > it changes to 1 and add to the next counted before it.)
3. 78.056 (since the number is less it turns to zero and it has no significance)

 Example 2.2: Give 57.9945 correct to (a) 2dp (b) 4dp
Solution:
(a) 57.99 (2 d.p.)
(b) 57.9945 (4 d.p.)
2.2    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 leas or sixth significant figure.er
987654
1^sts.f.2^nds.f.3^rds.f.4^ths.f.5^ths.f.6^ths.f.
Numbers less than zero
For example 0.000007685 is given to 8 decimal places. The zero before the decimal number means that there are no units, and the 5 zeros after the decimal point mean that they are insignificant figures. Therefore the most significant number or first significant is 7 follow by 6 and 8.

 0. 0 0 0 0 0 7 6 8
                 1sf 2sf 3sf
Note: the first significant figure is always the first non-zero figure as you read a number from the left

 Guide to round off numbers
To correct a number to a specific number of significant figure

1. Look for the required significant figure
2. Look at the next significant figure to the right (i.e. the decider)
3. If the decider is 5 or more round up but if it is less than 5 add nothing

 
 Example 2.3:Give 4540 correct to (a) 1 s.f (b) 2 sf (c) 3 s.f
Solution:
Note the figures above, it helps just follow the figure correctly.

1. 4540 = 5000 (the reason for getting 8000.after counting 7 the next number is 5 which will turn to 1 and add to the 7 counted and the other numbers turn to zeros).
2. 4540 = 4500 (after counting 2 s.f the next number is 6 which turn to 1 and add to 5 to be 6 and the rest turn to zeros.
3. 4540 = 4540 (after counting 3 s.f the next is 4 which turn to zero).

 Example 2.4: Convert 0.00005791 to (a) 2 s.f (b) 3 s.f
Solution:
(a) 0.000058
(b) 0.0000579

 
 2.3    Rounding Decimals to the Nearest, Tenth, Hundredth, and Thousandths and Whole.

 Example2.5:Give474.4547correcttothenearest
a.    Tenth
b.    Hundredth
c.    Thousandth
Solution:
Notethatthecountingstartsafterthepoint.

1. 474.4547=474.5(sincethenextnumberaftercountingis5/>itturnsto1andaddtothecounted4)
2. 474.4547=474.45
3. 474.4547=474.455

 Example 2.6:Roundoff
(a)13.73
(b)34.245tothe nearest wholenumber.

 Solution:

1. 13.73=14(sincethewholeis13thenextnumberisdecmalwhichis7,itwillbeturnto1andaddto13tomakeit14).
2. 34.245=34(sincethenextislessthan5thenitisinsignificant).

 ASSIGNMENT:     ESSENTIAL MATHEMATICS BOOK 1
EXERCISE 8.5 page 89 NO 2(a,b,c,d), 5+ (a,b,c)