The document summarizes key concepts about decimals including: - How to represent fractions as decimals by moving the decimal point. - Place value of decimals including tenths, hundredths, thousandths. - Rules for adding, subtracting, multiplying and dividing decimals including ensuring decimal points are aligned. - Rounding decimals to various place values. - Solving multi-step word problems involving decimals using multiple arithmetic operations.

1. CHAPTER 4CHAPTER 4
DECIMALSDECIMALS

2. Sub-topicsSub-topics
4.1 Decimals and Fractions4.1 Decimals and Fractions
4.2 Place Value and Value of Digit4.2 Place Value and Value of Digit
4.3 Addition and Subtraction4.3 Addition and Subtraction
4.4 Multiplication and Division4.4 Multiplication and Division
4.5 Combined Operations4.5 Combined Operations

3. 4.1 DECIMALS AND FRACTIONS4.1 DECIMALS AND FRACTIONS
How to represent fractions withHow to represent fractions with
denominators 10, 100 and 1 000 asdenominators 10, 100 and 1 000 as
decimals.decimals.
Exampels:Exampels:
a.a. 77 = 0.7= 0.7 Move the decimal pointMove the decimal point
1010 1 place to the left.1 place to the left.
11
zerozero

4. b.b. 7676 = 0.76= 0.76
100100
c.c. 153153 = 0.153= 0.153
10001000
d.d. 4848 = 0.0048= 0.0048
1000010000
Move the decimal point 2
places to the right
Move the decimal point 3
places to the right
Move the decimal point 4
places to the right
2 zeros
3 zeros
4 zeros

5. How to read decimals.How to read decimals.
1.1. 0.20.2 is read asis read as zero point two.zero point two.
2.2. 0.0050.005 is read asis read as zero point zero zerozero point zero zero
five.five.
3.3. 5.7015.701 is read asis read as five point seven zerofive point seven zero
one.one.
4.4. 17.3217.32 is read asis read as seventeen point threeseventeen point three
two.two.
5.5. 24. 57924. 579 is read asis read as twenty-four point fivetwenty-four point five
seven nine.seven nine.

6. How to change fractionsHow to change fractions
to decimals.to decimals.
a.a. 77
99
0.770.77
99)7.00)7.00
6 36 3
7070
6363
77
= 0.77= 0.77
b.b. 1212
77
1.711.71
77)12.00)12.00
77
5 05 0
4 94 9
1010
77
33
= 1.71= 1.71

7. Place Value for Whole NumbersPlace Value for Whole Numbers
1.1. UnitsUnits
2.2. TensTens
3.3. HundredsHundreds
4.4. ThousandsThousands
5.5. Ten ThousandsTen Thousands
6.6. Hundred ThousandsHundred Thousands
7.7. MillionsMillions
4.2 PLACE VALUE AND4.2 PLACE VALUE AND
VALUE OF DIGITVALUE OF DIGIT

8. Place Value for DecimalsPlace Value for Decimals
1.1. Tenths – it is over tenTenths – it is over ten
2.2. Hundredths – it is over hundredHundredths – it is over hundred
3.3. Thousandths – it is over thousandThousandths – it is over thousand
4.4. Ten thousandths – it is over tenTen thousandths – it is over ten
thousandthousand
5.5. Hundred thousandths – it is overHundred thousandths – it is over
hundred thousandhundred thousand

9. 4.2 PLACE VALUE AND VALUE OF DIGIT4.2 PLACE VALUE AND VALUE OF DIGIT
To state the place value and the value of eachTo state the place value and the value of each
digit in decimals.digit in decimals.
PlacePlace
ValueValue
TensTens UnitsUnits PP
oo
ii
nn
tt
TenthsTenths
11
1010
HundredthsHundredths
11
100100
ThousandthsThousandths
11
1 0001 000
TenTen
ThousandthsThousandths
11
10 00010 000
HundredHundred
ThousandthsThousandths
11
100 000100 000
0.3280.328 00 .. 33 22 88
ValueValue 00 .. 0.30.3 0.020.02 0.0080.008
53.9030753.90307
55 33 .. 99 00 33 00 77
ValueValue 5050 33 .. 0.90.9 0.000.00 0.0030.003 0.00000.0000 0.000070.00007
Worksheet Answer

10. State the place value for the decimals placeState the place value for the decimals place
Place Value
Tens Units P
oi
nt
Tenths
1
10
Hundredths
1
100
Thousandths
1
1 000
Ten Thousandths
1
10 000
Hundred
Thousandths
1
100 000
0.431
8.037
0.04250
23.10457
70.05065
0 . 4 3 1
8 .
.
.
.
4
4
3
3
0
0 0 0
0
0 0 0
7
7
7
2
2
5
5
5 5
1
6

11. State the value of digit that underlined in theState the value of digit that underlined in the
correct place.correct place.
Value of
Digit
Tens Units P
o
i
n
t
Tenths
1
10
Hundredths
1
100
Thousandths
1
1 000
Ten
Thousandths
1
10 000
Hundred
Thousandths
1
100 000
49.26
672.59
5.639
19.215
0.0069
10
.
.
.
.
.
0.06
0.5
0.009
0.0009

12. To compare andTo compare and
arrange decimals.arrange decimals.
a.a. Arrange in increasingArrange in increasing
order.order.
Example:Example:
3.57, 0.546, 4.932, 0.023.57, 0.546, 4.932, 0.02
3.573.57
0.5460.546
4.9324.932
0.020.02
0.02, 0.546, 3.57, 4.9320.02, 0.546, 3.57, 4.932
b. Arrange in decreasingb. Arrange in decreasing
order.order.
Example:Example:
0.45, 4.501, 0.064, 1.0020.45, 4.501, 0.064, 1.002
0.450.45
4.5014.501
0.0640.064
1.0021.002
4.501, 1.002, 0.45, 0.0644.501, 1.002, 0.45, 0.064
Arrange
decimals in
vertical order
and the points
in vertical line
Arrange
decimals in
vertical order
and the points
in vertical line
Worksheet Answer

13. Rearrange the following decimals in increasingRearrange the following decimals in increasing
order.order.
a. 0.92, 0.95, 0.91, 0.94, 0.93a. 0.92, 0.95, 0.91, 0.94, 0.93
0.91, 0.92, 0.93, 0.94, 0.950.91, 0.92, 0.93, 0.94, 0.95
b. 31.0, 31.1, 31.3, 30.7, 30.3b. 31.0, 31.1, 31.3, 30.7, 30.3
30.3, 30.7, 31.0, 31.1, 31.330.3, 30.7, 31.0, 31.1, 31.3
c. 0.1, 0.4, 1.3, 0.25, 1.55c. 0.1, 0.4, 1.3, 0.25, 1.55
0.1, 0.25, 0.4, 1.3, 1.550.1, 0.25, 0.4, 1.3, 1.55
d. 120.2, 121.4, 119.9, 130.3, 107.6d. 120.2, 121.4, 119.9, 130.3, 107.6
107.6, 119.9, 120.2, 121.4, 130.3107.6, 119.9, 120.2, 121.4, 130.3

14. Rearrange the following decimals inRearrange the following decimals in
decreasing order.decreasing order.
a.a.

15. Complete the number lines.Complete the number lines.

16. To round off decimals.To round off decimals.
Rules:Rules:
a.a. equal to or greater than 5, add 1equal to or greater than 5, add 1 to theto the
digit to be rounded off and delete alldigit to be rounded off and delete all
digits to the right of it.digits to the right of it.
b.b. less than 5, do not change the digitless than 5, do not change the digit toto
be rounded off and delete all digits tobe rounded off and delete all digits to
the right of it.the right of it.

17. Examples:Examples:
Round off 0.63281 toRound off 0.63281 to
a. whole numbera. whole number
c. 2 decimal placesc. 2 decimal places
Solution:Solution:
a. 0.63281 =a. 0.63281 =
b. 0.63281 =b. 0.63281 =
c. 0.63281 =c. 0.63281 =
d. 0.63281 =d. 0.63281 =
b. 1 decimal placeb. 1 decimal place
d. 3 decimal placesd. 3 decimal places
1 (whole number)1 (whole number)
0.6 (1 decimal place)0.6 (1 decimal place)
0.63 (2 decimal places)0.63 (2 decimal places)
0.633 (3 decimal places)0.633 (3 decimal places)
Digit to be
rounded off
The tenths digit is greater than 5. Add 1 to the
units digit (0) and delete all digits to the right of 0.
The hundredths digit is less than 5. Do not change
tenths digit (6) and delete all digits to the right of 6.
Digit to be
rounded off
Digit to be
rounded off
Digit to be
rounded off
The thousandths digit is less than 5. Do not change
thousandths digit (3) and delete all digits to the right of 3.
The ten thousandths digit is greater than 5. Add 1 to the
thousandths units digit (2) and delete all digits to the right of 2.
Worksheet

18. 4.3 ADDITION AND SUBTRACTION4.3 ADDITION AND SUBTRACTION
Addition:Addition:
Examples:Examples:
1.1. 12.08 + 0.783 =12.08 + 0.783 =
12.08012.080
++ 0.7830.783
12.86312.863
2. 3.76 + 0.0204 +2. 3.76 + 0.0204 +
13. 931 =13. 931 =
3.76003.7600
0.02040.0204
++ 13.931013.9310
17.711417.7114
Put 1
zero
Make sure those
point in vertical line
Put 2
zeros
Put 1
zero

19. Subtraction:Subtraction:
Examples:Examples:
1.1. 5.87 – 0.536 =5.87 – 0.536 =
5.8705.870
–– 0.5360.536
5.3345.334
2. 12.84 – 0.305 –2. 12.84 – 0.305 –
6.0936 =6.0936 =
12.84012.840
–– 0.3050.305
12.535012.5350
–– 6.09366.0936
6.44146.4414
Put 1
zero
Make sure those
point in vertical line
Put 1
zero
Put 1
zero

20. 4.4 MULTIPLICATION AND DIVISION4.4 MULTIPLICATION AND DIVISION
Multiplication:Multiplication:
Examples:Examples:
1.1. 13.98 x 21 =13.98 x 21 =
13.9813.98
xx 2121
13981398 2+02+0
++ 27962796
293.58293.58
2. 3.8 x 12.3 x 0.5 =2. 3.8 x 12.3 x 0.5 =
3.83.8
xx 12.312.3
11 411 4
7676 1+11+1
++38 .38 .
46.7446.74
xx 0.50.5
23.37023.370 2+12+1
2 decimal place
0 decimal place
2 decimal place
1 decimal place
1 decimal place
2 decimal place
1 decimal place
3 decimal place

21. Division:Division:
Examples:Examples:
1. 12.0321. 12.032 ÷ 4 =÷ 4 =
3.0083.008
4)12.0324)12.032
1212
0 00 0
0 00 0
0303
0000
3232
3232
. .. .
= 3.008= 3.008
2. 1.98542. 1.9854 ÷ 100 =÷ 100 =
1.98541.9854 ÷ 100÷ 100
= 0.019854= 0.019854
3. 35.7 ÷ 1 000 =3. 35.7 ÷ 1 000 =
35.7 ÷ 1 00035.7 ÷ 1 000
= 0.0357= 0.0357
2 zeros
Move 2 places
to left
Move 3 places
to left

22. 4. 16.324. 16.32 ÷ 1.6 =÷ 1.6 =
16.32 ÷ 1.616.32 ÷ 1.6
10.210.2
16)163.216)163.2
1616
0303
0000
3 23 2
3 23 2
....
= 10.2= 10.2
5.5. 25.2125.21 ÷÷ 22 ==
33
= 25.21 x= 25.21 x 33
22
== 75.6375.63
22
37.81537.815
22)75.630)75.630
66
1515
1414
1 61 6
1 61 6
0303
0202
1010
1010
....
= 37.815= 37.815
Both, shift
the decimal
point 1
place to the
right

23. 4.5 COMBINED OPERATIONS4.5 COMBINED OPERATIONS
1.1. 32.87 + 2.56 – 16.963 =32.87 + 2.56 – 16.963 =
32.8732.87
+ 2.56+ 2.56
35.4335.43
- 16.963- 16.963
18.46718.467
=18.467=18.467
2.2. 15.73 – 4.825 + 41.9 =15.73 – 4.825 + 41.9 =
15.7315.73
-- 4.8254.825
10.90510.905
++ 41.941.9
52.80552.805
= 52.805= 52.805

24. 3.3. 5.4 x 1.955.4 x 1.95 ÷ 4.2 =÷ 4.2 =
5.45.4
x 1.95x 1.95
27 027 0
486486
+54+54
10.53010.530
2.5072.507
42)105.30042)105.300
8484
21 321 3
21 021 0
3030
0000
300300
294294
66
= 2.507= 2.507
4.4. 3.123.12 ÷ 5.5 x 6.73 =÷ 5.5 x 6.73 =
0.5670.567
55)31.20055)31.200
27 527 5
3 703 70
3 303 30
400400
385385
1515
0.5670.567
x 6.73x 6.73
17011701
39693969
+3402+3402
3.815913.81591
= 3.81591= 3.81591

25. 5. 2.67 x5. 2.67 x (5.4 – 3.6)(5.4 – 3.6) + 7.85+ 7.85 ÷ 1.9 =÷ 1.9 =
== 2.67 x 1.82.67 x 1.8 ++ 7.85 ÷ 1.97.85 ÷ 1.9
= 4.806 + 4.132= 4.806 + 4.132
= 8.938= 8.938
5.4 – 3.6 = 1.8
7.85 ÷ 1.9 = 4.132
2.67 x 1.8 = 4.806