CBSE Class 4 Maths Decimals Worksheet

LEARNING OBJECTIVES

This lesson will help you to:—
• understand what is a decimal.
• convert fractions into decimal.
• convert decimals into fractions.
• expanded from of decimals
• like and Unlike decimals
• operation on decimals

Historical Facts
• The word decimal originates from the Latin word ‘Decem’ which means ‘tenth’. Decimal number system is a positional notation with base ten, which was first used in India and was taken up by Arabs and introduced in Europe later

QUICK CONCEPT REVIEW
If we divide 17 by 4 we get 4.25

In 4.25, ‘.’ is called as a decimal. Let us understand it in detail.
Every decimal number has two parts, a whole number/ integral part and a decimal part. These two parts are separated by a dot (.) called decimal point.
For Example, 46.752 is a decimal fraction. It can be represented as

It is read as forty six point seven five two. The digits after the decimal point are to be read separately.

Decimal Place Value Chart
Just as we have a place value chart for whole number or natural number, we have a place value chart for decimals also.

ONE-TENTH
We can say one part of 10 equal parts is one-tenth. Onetenth is written as 1/10.
We also write it as 0.1.

Real Life Examples
• In today’s world all the quantities have been fractionalised whether it is money, distance, mass, capacity, time, temperature, etc. Wherever we have division, we have decimals.
Let’s go through some of the important uses of decimals.
Use of Decimals in Money Value
We know that,
100 paise = 1 rupee
• 1 paisa = 1/100 rupee or 0.01 rupee.
Example : Write Rupees 16 and 48 paise as rupees.
Solution : ` 16 and 48
p = ` 16.48

Use of Decimals in Measurement of Length 
We know that,
100 cm = 1 m
• 1 cm = 1/100 m or 0.01 m
1000 m = 1 km
1 m = 1/1000 km or 0.001km
Example : Write as decimals : 45 m 8 cm
Solution : 45 m 8 cm = 45.08 m

ONE-THOUSANDTH
One part of 1000 equal parts is one-thousandth. Onethousandth is written as 1/1000

So, 0.1, 0.01, 0.001 are called decimal numbers.

WRITING A FRACTION AS DECIMAL
The common fractions with denominators 10, 100 and 1000 can be written as decimal fractions.
For Example, (a) 6/10 is written as 0.6 (six-tenth)
(b) 12/100 is written as 0.12 (twelve-hundredth)
(c) 845/1000 is written as 0.845 (eight hundred forty five thousandth)

Try It!
Write 0.08 as a fraction.
The number of digits after the decimal point is 2. Hence, the denominator is 100 and the numerator is 8.
So, 0.08 = 8/100

WRITING A DECIMAL FRACTION AS COMMON FRACTION
For writing a decimal fraction as common fraction, the denominator is written with a digit followed by the number of zeroes equal to the number of digits after the decimal point and the numerator is the number given in the decimal fraction but without decimal point.

WRITE 0.102 AS A FRACTION
The number of digits after the decimal point is 3. Hence, the denominator is 1000 and numerator is 102.
So, 0 102 = 102/1000

LIKE AND UNLIKE DECIMALS
Like Decimals
Decimals having equal number of decimal places and called like decimals.
Example : 4.9, 13.5, 175.3 are like decimals.
Unlike Decimals
Unlike decimals are decimals having different number of decimal places.
Example : 7.8, 15.09, 1.789, 34.000 are unlike decimals.

Do You Know ?
• The place value system and the decimal system was developed in India in 100 BC.
• India invented the number system and zero was invented by Arybhatta.
• Zero is the only number known as so many names like zip, nil, nought

Converting Unlike Decimals into like Decimals
Example : In 17.8, 9.76, 14.379,
17.8 has one decimal place.
9.76 has two decimal places.
14.379 has three decimal places.
To make them like decimals add as many zeroes needed to make them equivalent decimals.
Hence, 17.800; 9.760; 14.379 are like decimals.

COMPARING AND ORDERING DECIMAL FRACTIONS
Rule 1 : To compare two given decimal fractions, compare the integral part. The decimal fraction with the greater integral part is greater.
Rule 2. If the integral parts are equal, compare the digits in the tenths place. If in the decimal part, digits in the tenths place and the digits in the hundredths place are equal, compare the digits in the thousandth place and so on.
Example : Compare 7.9 and 9.8
Solution : Integral part of 7.9 = 7, Integral part of 9.8 = 9
7 < 9, hence 7.9 < 9.8.
Example : Compare 18.9 and 18.2.
Solution : As the integral parts are equal, compare tenths part.
9 > 2, hence, 18.9 > 18.2

ADDITION OF DECIMALS
Example : Solve 8.4 + 0.78
    O t h
   8 4 0
+ 0 7 8      Step 1. Change into like decimals
   9 1 8      Step 2. Arrange them according to the place value.
Example : Solve 89.314 + 4.68
Solution : T O t h th
                 8 9 3 1 4
                 -  4 6 8 0
                 9 3 9 9 4

SUBTRACTION OF DECIMALS
Subtraction of decimals is also done in the same way like addition by arranging them in columns according to their place values.
Example : Solve 7 – 1.85
Solution : O t h
                 7 0 0
                -1 8 5
                 5 1 5
Example : Solve 59.814 – 3.99
Solution : T o t h th
                 5 9 8 1 4
                  - 3 9 9 0
                 5 5 8 2 4

Do You Know ?
• In decimal numbers, the number of digits does not make a number greater or smaller. Only the value of the highest place determines the value of the decimal number.

Question. Writing seventy five and two hundredth in decimals, we get
(a) 0.752
(b) 75.2
(c) 75.02
(d) 75.002
Answer : C

Question. 708/1000 is equal to
(a) 70.8
(b) 0.708
(c) 7.08
(d) 708
Answer : B

Question. 0.0752 is equal to
(a) 752/100
(b) 752/1000
(c) 752/10000
(d) 752/10
Answer : C

4. 45 + 2 + 3/100 =? 
(a) 45.23
(b) 452.3
(c) 4.523
(d) 47.03
Answer : D

Question. 0.69 is equal to
(a) 0.6900
(b) 0.069
(c) 0.0069
(d) 6.9
Answer : A

Question. In 605.32, 3 is in ________ place.
(a) Tenth
(b) Hundredth
(c) Thousandth
(d) None of these
Answer : A

Question. Expanded form of 69.302 is
(a) 60+9+ 3/10 + 2/100
(b) 60+9+ 3/10 + 2/1000
(c) 60 + 9/10 + 3/100 + 2/1000
(d) 60+9+ 3/1000 + 2/10
Answer : B

Question. Fill in the blank 0.57 ________ 0.0057
(a) =
(b) >
(c) <
(d) None of these
Answer : B

Question. Converting ₹ 356 paise into ₹ , we get
(a) ₹ 3.56
(b) ₹ 356
(c) ₹ 3.056
(d) ₹ 30056
Answer : A

Question. Converting 455 cm into metres we get
(a) 0.455
(b) 45.5
(c) 0.0455
(d) 4.55
Answer : D

Question. Wasim bought a pen for ₹ 450.25. If he had ₹ 569.90 with him, how much money he has left with?
(a) ₹ 219.60
(b) ₹ 119.65
(c) ₹ 210.80
(d) ₹ 119.50
Answer : B

Question. Ram distributed ₹ 680.60 among 6 cousins. Find the share of each.
(a) ₹ 113.43
(b) ₹ 103.40
(c) ₹ 110.65
(d) ₹ 240.05
Answer : A

Question. I had ₹ 8.53. My mother and father gave me ₹ 343.35 and ₹ 175.50 respectively.
How much total money I have now?
(a) ₹ 547.43
(b) ₹ 504.48
(c) ₹ 527.38
(d) ₹ 526.45
Answer : C

Question. Find the sum of ₹ 456.50, ₹ 345.75 and ₹ 802.25
(a) ₹ 1604.50
(b) ₹ 1200.80
(c) ₹ 1040.58
(d) ₹ 1640.50
Answer : A

Question. 8 Students want to donate ₹ 124.80 to a poor man. What is the contribution by each of them?
(a) ₹ 15.60
(b) ₹ 25.60
(c) ₹ 51.40
(d) ₹ 16.80
Answer : A

Question. Write 32 kg 19 g as decimals (in kg)
(a) 32.19
(b) 32.019
(c) 32.00019
(d) 321.9
Answer : B

Question. Write 40 Km 6 m as a decimal (in km)
(a) 40.006
(b) 40.6
(c) 40.06
(d) 40.0006
Answer : A

Question. Write 7 l 378 ml as a decimal. (in l)
(a) 7.0378
(b) 73.78
(c) 7.378
(d) 737.8
Answer : C

Question. Converting 4.62 m into cm, we get
(a) 462
(b) 4620
(c) 46200
(d) 0.462
Answer : A

Question. 0.67 + 0.006 + 0.7 = ?
(a) 11.37
(b) 13.76
(c) 0.1376
(d) 1.376
Answer : D

Question. 56.7 – 19.72 is equal to
(a) 3.698
(b) 36.98
(c) 13.45
(d) 37.02
Answer : B

Question. 7 + 13.05 + 118.016 is equal to
(a) 138.066
(b) 145.076
(c) 198.016
(d) 138.676
Answer : A

Question. 0.45 is greater than
(a) 0.945
(b) 0.6445
(c) 0.97
(d) 0.21
Answer : D

Question. 8 + 0.3 + 0.07 is equal to
(a) 18
(b) 83.07
(c) 8.37
(d) 0.837
Answer : C

Question. Converting 65 mm into cm, we get
(a) 6.5
(b) 0.65
(c) 0.065
(d) 16.50
Answer : A

Question. ₹ 27.50 = ________ paise
(a) 2705
(b) 2700
(c) 2075
(d) 2750
Answer : D

Question. 4.54 × 5.67 is equal to
(a) 25.7408
(b) 24.7408
(c) 25.7418
(d) 24.0418
Answer : C

Question. ₹ 5.50 = _________ paise
(a) 550
(b) 505
(c) 500
(d) 55
Answer : A

Please click on below link to download CBSE Class 4 Maths Decimals Worksheet