decimals
TRANSCRIPT
CHAPTER 4CHAPTER 4
DECIMALSDECIMALS
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
4.1 DECIMALS AND FRACTIONS4.1 DECIMALS AND FRACTIONS
How to represent fractions with How to represent fractions with denominators 10, 100 and 1 000 as denominators 10, 100 and 1 000 as decimals.decimals.
Exampels:Exampels:
a. a. 77 = 0.7 = 0.7 Move the decimal pointMove the decimal point
10 10 1 place to the left.1 place to the left.
1 1
zerozero
b.b. 7676 = 0.76 = 0.76
100 100
c.c. 153153 = 0.153 = 0.153
10001000
d.d. 48 48 = 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
How to read decimals.How to read decimals.
1.1. 0.20.2 is read as is read as zero point two.zero point two.
2.2. 0.0050.005 is read as is read as zero point zero zero zero point zero zero five.five.
3.3. 5.7015.701 is read as is read as five point seven zero five point seven zero one.one.
4.4. 17.3217.32 is read as is read as seventeen point three seventeen point three two.two.
5.5. 24. 57924. 579 is read as is read as twenty-four point five twenty-four point five seven nine.seven nine.
How to change fractions How to change fractions to decimals.to decimals.a. a. 77 99
0.770.7799)7.00)7.00 6 36 3 7070 6363 77
= 0.77= 0.77
b.b. 1212 77
1.711.7177)12.00)12.00 77 5 05 0 4 94 9 1010 77 33
= 1.71= 1.71
Place Value for Whole NumbersPlace Value for Whole Numbers
1.1. UnitsUnits2.2. TensTens3.3. HundredsHundreds4.4. ThousandsThousands5.5. Ten ThousandsTen Thousands6.6. Hundred ThousandsHundred Thousands7.7. MillionsMillions
4.2 PLACE VALUE AND 4.2 PLACE VALUE AND VALUE OF DIGITVALUE OF DIGIT
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 ten Ten thousandths – it is over ten thousandthousand
5.5. Hundred thousandths – it is over Hundred thousandths – it is over hundred thousandhundred thousand
4.2 PLACE VALUE AND VALUE OF DIGIT4.2 PLACE VALUE AND VALUE OF DIGITTo state the place value and the value of each To state the place value and the value of each digit in decimals.digit in decimals.
Place Place ValueValue
TensTens UnitsUnits PPooiinntt
TenthsTenths
11
1010
HundredthsHundredths
11
100100
ThousandthsThousandths
11
1 0001 000
Ten Ten ThousandthsThousandths
11
10 00010 000
Hundred Hundred 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
State the place value for the decimals placeState the place value for the decimals place
Place ValueTens Units P
oint
Tenths1
10
Hundredths1
100
Thousandths1
1 000
Ten Thousandths1
10 000
Hundred Thousandths
1100 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
State the value of digit that underlined in the State the value of digit that underlined in the correct place.correct place.
Value of Digit
Tens Units Point
Tenths1
10
Hundredths1
100
Thousandths1
1 000
TenThousandths
110 000
HundredThousandths
1100 000
49.26
672.59
5.639
19.215
0.0069
10
.
.
.
.
.
0.06
0.5
0.009
0.0009
To compare and To compare and arrange decimals.arrange decimals.
a.a. Arrange in increasing Arrange 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
4.9324.9320.020.02
0.02, 0.546, 3.57, 4.9320.02, 0.546, 3.57, 4.932
b. Arrange in decreasing b. Arrange in decreasing order.order.Example:Example:0.45, 4.501, 0.064, 1.0020.45, 4.501, 0.064, 1.002
0.450.454.5014.5010.0640.0641.0021.002
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
Rearrange the following decimals in increasing Rearrange 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
Rearrange the following decimals in Rearrange the following decimals in decreasing order.decreasing order.
a. a.
Complete the number lines.Complete the number lines.
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 to the the digit to be rounded off and delete all digit 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 to to be rounded off and delete all digits to be rounded off and delete all digits to the right of it.the right of it.
Examples:Examples:Round off 0.63281 toRound off 0.63281 toa. whole numbera. whole number
c. 2 decimal placesc. 2 decimal placesSolution: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 placed. 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
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
+ + 0.783 0.783
12.86312.863
2. 3.76 + 0.0204 + 2. 3.76 + 0.0204 +
13. 931 =13. 931 =
3.76003.7600
0.02040.0204
+ + 13.9310 13.9310
17.711417.7114
Put 1 zero
Make sure those point in vertical line
Put 2 zeros
Put 1 zero
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
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
x x 21 21
13981398 2+02+0
+ + 2796 2796
293.58293.58
2. 3.8 x 12.3 x 0.5 =2. 3.8 x 12.3 x 0.5 =
3.83.8
x x 12.312.3
11 411 4
7676 1+1 1+1
++38 .38 .
46.7446.74
x x 0.5 0.5
23.37023.370 2+1 2+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
Division:Division:Examples:Examples:
1. 12.032 1. 12.032 ÷ 4 =÷ 4 =
3.0083.008 4)12.0324)12.032 1212 0 00 0 0 00 0
03030000
32323232
. .. . = 3.008= 3.008
2. 1.9854 2. 1.9854 ÷ 100 =÷ 100 =
1.9854 1.9854 ÷ 100 ÷ 100
= 0.019854= 0.019854
3. 35.7 ÷ 1 000 =3. 35.7 ÷ 1 000 =
35.7 ÷ 1 000 35.7 ÷ 1 000
= 0.0357= 0.0357
2 zerosMove 2 places
to left
Move 3 places to left
4. 16.32 4. 16.32 ÷ 1.6 =÷ 1.6 =
16.32 ÷ 1.6 16.32 ÷ 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. 25.21 25.21 ÷ ÷ 22 = = 3 3 = 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
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
-- 4.825 4.825
10.90510.905
++ 41.941.9
52.80552.805
= 52.805= 52.805
3.3. 5.4 x 1.95 5.4 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 3 21 3 21 021 0
3030 0000 300300 294294 66
= 2.507= 2.507
4.4. 3.12 3.12 ÷ 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
5. 2.67 x 5. 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