## NCERT Class VI Mathematics Chapter 8 Decimals

National Council of Educational Research and Training (NCERT) Book for Class VI
Subject: Mathematics
Chapter: Chapter 8 – Decimals

Class VI NCERT Mathematics Text Book Chapter 8 Decimals is given below.

8.1 Introduction

Savita and Shama were going to market to buy some stationary items. Savita said, “I have 5 rupees and 75 paise”. Shama said, “I have 7 rupees and 50 paise”.

Representing Decimals on number line

We represented fractions on a number line. Let us now represent decimals too on a number line. Let us represent 0.6 on a number line.

We know that 0.6 is more than zero but less than one. There are 6 tenths in it. Divide the unit length between 0 and 1 into 10 equal parts and take 6 parts as shown below :

Write five numbers between 0 and 1 and show them on the number line.

Can you now represent 2.3 on a number line? Check, how many ones and tenths are there in 2.3. Where will it lie on the number line?

Show 1.  4 on the number line.

Example 1 : Write the following numbers in the place value table : (a) 20.5 (b) 4.2

Solution : Let us make a common place value table, assigning appropriate place value to the digits in the given numbers. We have,

Fractions as decimals

We have already seen how a fraction with denominator 10 can be represented using decimals.

2. Write the following decimals in the place value table.

(a) 19.4     (b) 0.3      (c) 10.6    (d) 205.9

3. Write each of the following as decimals :

(a) Seven-tenths          (b) Two tens and nine-tenths

(c) Fourteen point six   (d) One hundred and two ones

(e) Six hundred point eight

Example 10 : Write each of the following as a decimal.

(a) Three hundred six and seven-hundredths

(b) Eleven point two three five

(c) Nine and twenty five thousandths

3. Write the following decimals in the place value table.

(a) 0.29       (b) 2.08     (c) 19.60    (d) 148.32     (e) 200.812

4. Write each of the following as decimals.

(a) 20 + 9 + 4/10 + 1/100       (b) 137 + 5/100   (c) 7/10 + 6/100 + 4/1000

(d) 23  +  2/10 + 6/1000         (e) 700 +  20 +  5 + 9/100

5. Write each of the following decimals in words.

(a) 0.03    (b) 1.20     (c) 108.56    (d) 10.07    (e) 0.032    (f) 5.008

6. Between which two numbers in tenths place on the number line does each of the given number lie?

(a) 0.06    (b) 0.45     (c) 0.19     (d) 0.66    (e) 0.92    (f) 0.57

7. Write as fractions in lowest terms.

(a) 0.60     (b) 0.05    (c) 0.75     (d) 0.18   (e) 0.25   (f) 0.125

(g) 0.066

8.4 Comparing Decimals

Can you tell which is greater, 0.07 or 0.1?

Take two pieces of square papers of the same size. Divide them into 100 equal parts. For 0.07 we have to shade 7 parts out of 100.

Now, 0.1 =1/10 = 10/100 , so, for 0.1, shade 10 parts out 100.

This means 0.1>0.07

Let us now compare the numbers 32.55 and 32.5. In this case , we first compare the whole part. We see that the whole part for both the nunbers is 32
and, hence, equal.

We, however, know that the two numbers are not equal. So, we now compare the tenth part. We find that for 32.55 and 32.5, the tenth part is also equal, then we compare the hundredth part.

We find,

32.55 = 32 +5/10 + 5/100 and 32.5 = 32 + 5/10 + 0/100 , therefore, 32.55>32.5 as the hundredth part of 32.55 is more.

Example 11 : Which is greater?

(a) 1 or 0.99       (b) 1.09 or 1.093

Solution : (a) 1 = 1 + 0/10 + 0/100    ; 0 .99 = 9/10  + 9/100

The whole part of 1 is greater than that of 0.99.

Therefore, 1 > 0.99

(b) 1. 09 +  1 + 0/10 + 9/100 + 0/1000  ; 1. 093 =  1+ 0/10 + 9/100 + 3/1000

In this case, the two numbers have same parts upto hundredth. But the thousandths part of 1.093 is greater than that of 1.09. Therefore, 1.093 > 1.09.

EXERCISE 8.3

1. Which is greater?

(a) 0.3 or 0.4 (b) 0.07 or 0.02 (c) 3 or 0.8 (d) 0.5 or 0.05

(e) 1.23 or 1.2 (f) 0.099 or 0.19 (g) 1.5 or 1.50 (h) 1.431 or 1.490

(i) 3.3 or 3.300 (j) 5.64 or 5.603

2. Make five more examples and find the greater number from them.

EXERCISE 8.4

1. Express as rupees using decimals.

(a) 5 paise (b) 75 paise (c) 20 paise

(d) 50 rupees 90 paise (e) 725 paise

2. Express as metres using decimals.

(a) 15 cm (b) 6 cm (c) 2 m 45 cm

(d) 9 m 7 cm (e) 419 cm

3. Express as cm using decimals.

(a) 5 mm (b) 60 mm (c) 164 mm

(d) 9 cm 8 mm (e) 93 mm

4. Express as km using decimals.

(a) 8 m (b) 88 m (c) 8888 m

(d) 70 km 5 m

5. Express as kg using decimals.

(a) 2 g (b) 100 g (c) 3750 g

(d) 5 kg 8 g (e) 26 kg 50 g

Do This

Take a square and divide it into 100 equal parts.

EXERCISE 8.5

1. Find the sum in each of the following :

(a) 0.007 + 8.5 + 30.08

(b) 15 + 0.632 + 13.8

(c) 27.076 + 0.55 + 0.004

(d) 25.65 + 9.005 + 3.7

(e) 0.75 + 10.425 + 2

(f) 280.69 + 25.2 + 38

2. Rashid spent Rs 35.75 for Maths book and Rs 32.60 for Science book. Find the total amount spent by Rashid.

3. Radhika’s mother gave her Rs 10.50 and her father gave her Rs 15.80, find the total amount given to Radhika by the parents.

4. Nasreen bought 3 m 20 cm cloth for her shirt and 2 m 5 cm cloth for her trouser. Find the total length of cloth bought by her.

5. Naresh walked 2 km 35 m in the morning and 1 km 7 m in the evening. How much distance did he walk in all?

6. Sunita travelled 15 km 268 m by bus, 7 km 7 m by car and 500 m on foot in order to reach her school. How far is her school from her residence?

7. Ravi purchased 5 kg 400 g rice, 2 kg 20 g sugar and 10 kg 850g flour. Find the total weight of his purchases

Example 15 : Abhishek had Rs 7.45. He bought toffees for Rs 5.30. Find the

balance amount left with Abhishek.

Solution : Total amount of money = Rs 7.45

Amount spent on toffees = Rs 5.30

Balance amount of money = Rs 7.45 – Rs 5.30 = Rs 2.15

Example 16 : Urmila’s school is at a distance of 5 km 350 m from her house. She travels 1 km 70 m on foot and the rest by bus. How much distance does she travel by bus?

Solution : Total distance of school from the house = 5.350 km

Distance travelled on foot = 1.070 km

Therefore, distance travelled by bus = 5.350 km – 1.070 km = 4.280 km

Thus, distance travelled by bus = 4.280 km or 4 km 280 m

Example 17 : Kanchan bought a watermelon weighing 5 kg 200 g. Out of this she gave 2 kg 750 g to her neighbour. What is the weight of the watermelon left with Ruby?

Solution : Total weight of the watermelon = 5.200 kg

Watermelon given to the neighbour = 2.750 kg

Therefore, weight of the remaining watermelon = 5.200 kg – 2.750 kg = 2.450 kg

What have we discussed?

1. To understand the parts of one whole (i.e. a unit) we represent a unit by a block. One block divided into 10 equal parts means each part is 1/10 (one-tenth) of a unit. It can be written as 0.1 in decimal notation. The dot represents the decimal point and it comes between the units place and the tenths place.

2. Every fraction with denominator 10 can be written in decimal notation and vice-versa.

3. One block divided into 100 equal parts means each part is ( ) 1/100 (one-hundredth) of a unit. It can be written as 0.01 in decimal notation.

4. Every fraction with denominator 100 can be written in decimal notation and vice-versa.

5. In the place value table, as we go from left to the right, the multiplying factor becomes 1/10 of the previous factor. The place value table can be further extended from hundredths to 1/10  of hundredths i.e. thousandths (1/1000), which is written as 0.001 in decimal notation.

6. All decimals can also be represented on a number line.

7. Every decimal can be written as a fraction.

8. Any two decimal numbers can be compared among themselves. The comparison can start with the whole part. If the whole parts are equal then the tenth parts can be compared and so on.

9. Decimals are used in many ways in our lives. For example, in representing units of money, length and weight.