Class 6 Maths - Decimals NCERT Solutions

Chapter 8: Decimals (NCERT Solutions)

Exercise 8.1 (Tenths)

Q1. Write 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

(a) 0.7

(b) 20.9

(d) 102 (no decimal part; but written as 102.0)

(e) 600.8

Q2. Write the following decimals in the place value table:
(a) 19.4 (b) 0.3 (c) 10.6 (d) 205.9

Number	Hundreds	Tens	Ones	Tenths
19.4	0	1	9	4
0.3	0	0	0	3
10.6	0	1	0	6
205.9	2	0	5	9

Q3. Write each of the following as decimals:
(a) 5/10 (b) 3 + 7/10 (c) 200 + 60 + 5 + 1/10 (d) 70 + 8/10

(a) 5/10 = 0.5

(b) 3 + 7/10 = 3.7

(d) 70 + 8/10 = 70.8

Q4. Write each of the following as decimals:
(a) Eleven point two (b) Nine point five (c) Twelve point three seven

(a) 11.2

(b) 9.5

Exercise 8.2 (Hundredths)

Q1. Complete the table with the appropriate decimal:

Hundreds	Tens	Ones	Tenths	Hundredths	Decimal
0	0	3	2	5	3.25
1	0	2	6	3	102.63
0	3	0	0	5	30.05

Q2. Write as decimals:
(a) 5/100 (b) 15/100 (c) 27 + 6/100 (d) 9/100 (e) 4/10 + 8/100

(a) 5/100 = 0.05

(b) 15/100 = 0.15

(d) 9/100 = 0.09

(e) 4/10 + 8/100 = 40/100 + 8/100 = 48/100 = 0.48

Exercise 8.3 (Comparing Decimals)

Q1. 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

(a) 0.4 (4 tenths > 3 tenths)

(b) 0.07 (7 hundredths > 2 hundredths)

(d) 0.5 (0.50 > 0.05)

(e) 1.23 (1.23 > 1.20)

(f) 0.19 (0.190 > 0.099)

Q2. Make five more pairs and write as above.

(i) 0.8 > 0.08 (ii) 1.01 > 0.99 (iii) 0.5 > 0.49 (iv) 3.5 > 3.05 (v) 10.1 > 9.9

Q3. Arrange in ascending order:
(a) 0.4, 0.57, 0.29 (b) 0.10, 0.081, 0.009 (c) 1.1, 2.1, 0.111 (d) 2.2, 2.02, 2.222, 2.22

(a) 0.29, 0.4, 0.57

(b) 0.009, 0.081, 0.10

(d) 2.02, 2.2, 2.22, 2.222

Exercise 8.4 (Fractions as Decimals)

Q1. Express as rupees using decimals:
(a) 5 paise (b) 75 paise (c) 20 paise (d) 50 rupees 90 paise (e) 725 paise

(a) 5 paise = 5/100 rupees = Rs. 0.05

(b) 75 paise = 75/100 = Rs. 0.75

(d) 50 rupees 90 paise = Rs. 50.90

(e) 725 paise = 700 paise + 25 paise = 7 rupees 25 paise = Rs. 7.25

Q2. Express as metres using decimals:
(a) 15 cm (b) 6 cm (c) 2 m 45 cm (d) 9 m 7 cm (e) 419 cm

(a) 15 cm = 15/100 m = 0.15 m

(b) 6 cm = 0.06 m

(d) 9 m 7 cm = 9.07 m

(e) 419 cm = 400 cm + 19 cm = 4 m + 0.19 m = 4.19 m

Q3. Express as km using decimals:
(a) 8 m (b) 88 m (c) 8888 m (d) 70 km 5 m

(a) 8 m = 8/1000 km = 0.008 km

(b) 88 m = 0.088 km

(d) 70 km 5 m = 70.005 km

Q4. Express as kg using decimals:
(a) 2 g (b) 100 g (c) 3750 g (d) 5 kg 8 g (e) 26 kg 50 g

(a) 2 g = 2/1000 kg = 0.002 kg

(b) 100 g = 100/1000 = 0.100 kg

(d) 5 kg 8 g = 5.008 kg

(e) 26 kg 50 g = 26.050 kg

Exercise 8.5 (Addition of Decimals)

Q1. 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

(a) 0.007 + 8.500 + 30.080 = 38.587

(b) 15.000 + 0.632 + 13.800 = 29.432

(d) 25.650 + 9.005 + 3.700 = 38.355

(e) 0.750 + 10.425 + 2.000 = 13.175

(f) 280.690 + 25.200 + 38.000 = 343.890

Q2. Rashid spent Rs. 35.75 for maths book and Rs. 32.60 for science book. Find the total amount spent by Rashid.

Total = 35.75 + 32.60 = Rs. 68.35.

Q3. 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.

Total = 10.50 + 15.80 = Rs. 26.30.

Exercise 8.6 (Subtraction of Decimals)

Q1. Subtract:
(a) 18.3 − 11.7 (b) 20.05 − 9.3 (c) 24 − 0.023 (d) 16.508 − 5.91 (e) 4.2 − 3.72

(a) 18.30 − 11.70 = 6.60

(b) 20.05 − 9.30 = 10.75

(d) 16.508 − 5.910 = 10.598

(e) 4.20 − 3.72 = 0.48

Q2. Raju bought a book worth Rs. 35.65. He gave Rs. 50 to the shopkeeper. How much change did he get back?

Change = 50.00 − 35.65 = Rs. 14.35.

Q3. Rani had Rs. 18.50. She spent Rs. 11.25 on one item and Rs. 3.30 on another. How much money is left with her?

Amount spent = 11.25 + 3.30 = 14.55.
Amount left = 18.50 − 14.55 = Rs. 3.95.

Q4. Tina had 20 m 5 cm long cloth. She cut 4 m 50 cm from it. What length of cloth remains?

20 m 5 cm = 20.05 m. 4 m 50 cm = 4.50 m.
Remaining = 20.05 − 4.50 = 15.55 m (15 m 55 cm).

Class 6 Maths - Decimals Practice Questions

Chapter 8: Decimals (Practice Questions)

RD Sharma / HOT Practice

Q1. Write the place value of each digit in 47.839.

4 → Tens place = 40
7 → Ones place = 7
8 → Tenths place = 0.8
3 → Hundredths place = 0.03
9 → Thousandths place = 0.009

Q2. Convert 5 and 3/4 into decimal form.

3/4 = 75/100 = 0.75.
5 and 3/4 = 5.75.

Q3. Arrange in descending order: 7.03, 7.30, 7.003, 7.330

All have same ones digit (7). Compare decimal parts:
7.330 > 7.30 > 7.03 > 7.003.
Descending: 7.330, 7.30, 7.03, 7.003.

Q4. A bag weighs 8 kg 350 g. Express its weight in kg as a decimal.

350 g = 350/1000 kg = 0.350 kg.
Total = 8.350 kg.

Q5. Add: 7.5 + 8.346 + 12.09 + 6.007

7.500 + 8.346 + 12.090 + 6.007 = 33.943.

Q6. Subtract: 100.5 − 47.638

100.500 − 47.638 = 52.862.

Q7. A runner completes three laps of distances 1.25 km, 0.875 km, and 1.4 km. What is the total distance?

1.250 + 0.875 + 1.400 = 3.525 km.

Q8. Shyam has Rs. 250.00. He spends Rs. 85.50 on food and Rs. 63.75 on books. How much is left?

Total spent = 85.50 + 63.75 = 149.25.
Left = 250.00 − 149.25 = Rs. 100.75.

Q9. Which is greater: 32.5 or 3.25? By how much?

32.5 is greater.
Difference = 32.50 − 3.25 = 29.25.

Q10. Convert 3 km 75 m to km expressed as a decimal.

75 m = 75/1000 km = 0.075 km.
Total = 3.075 km.

Q11. What decimal should be added to 1.9 to get 8.05?

Required decimal = 8.05 − 1.90 = 6.15.

Q12. Express 2.075 as a fraction in simplest form.

2.075 = 2075/1000.
HCF(2075, 1000) = 25.
2075/1000 = 83/40 = 83/40 (or 2 and 3/40).

Q13. The price of a pen is Rs. 3.75 and that of a pencil is Rs. 1.25. What is the cost of 4 pens and 3 pencils?

4 pens = 4 × 3.75 = Rs. 15.00.
3 pencils = 3 × 1.25 = Rs. 3.75.
Total = 15.00 + 3.75 = Rs. 18.75.

Q14. Write 0.875 as a fraction in simplest form.

0.875 = 875/1000. HCF(875, 1000) = 125.
875/1000 = 7/8.

Q15. Fill in the blanks: 3.7 = 3 + ___ /10 = ___ /10

3.7 = 3 + 7/10 = 37/10.

Q16. Between which two whole numbers does 4.7 lie? Which one is it closer to?

4.7 lies between 4 and 5.
4.7 is closer to 5 (since 0.7 > 0.5, so it is more than halfway to 5).

Q17. How many decimal places does 0.0050 have? Is it equal to 0.005?

0.0050 has 4 decimal places. It is equal to 0.005 (trailing zeros after the last significant digit do not change the value). Yes, 0.0050 = 0.005.

Q18. A piece of wire was 18.6 m long. Two pieces of 4.75 m and 6.5 m were cut from it. What remains?

Total cut = 4.75 + 6.50 = 11.25 m.
Remaining = 18.6 − 11.25 = 7.35 m.

Q19. The weight of 3 packages is 2.5 kg, 3.25 kg, and 1.075 kg. What is their total weight?

2.500 + 3.250 + 1.075 = 6.825 kg.

Q20. Evaluate: 5.6 + 3.47 − 2.9 + 0.08

5.60 + 3.47 = 9.07.
9.07 − 2.90 = 6.17.
6.17 + 0.08 = 6.25.

Class 6 Maths - Decimals Summary

Chapter 8: Decimals (Concepts & Summary)

1. Decimal Place Value Chart

Thousands	Hundreds	Tens	Ones	• (Decimal point)	Tenths	Hundredths	Thousandths
1000	100	10	1		1/10	1/100	1/1000

Example: In 24.756 → 2 (tens), 4 (ones), 7 (tenths), 5 (hundredths), 6 (thousandths).

2. Comparing Decimals

Compare the whole number parts first. The one with the larger whole number is greater.
If whole parts are equal, compare the tenths digits first.
If tenths are also equal, compare hundredths, then thousandths.

Tip: Add trailing zeros to make decimal places equal for easier comparison.
e.g., 0.3 = 0.300 and 0.29 = 0.290 → 0.300 > 0.290.

3. Fractions ↔ Decimals (Measurement Conversions)

Conversion	Rule	Example
Paise → Rupees	Divide by 100	75 p = Rs. 0.75
cm → m	Divide by 100	45 cm = 0.45 m
m → km	Divide by 1000	350 m = 0.350 km
g → kg	Divide by 1000	750 g = 0.750 kg
ml → litres	Divide by 1000	250 ml = 0.250 L

4. Addition & Subtraction of Decimals

Write the decimals in a column with decimal points aligned vertically.
Fill in the missing decimal places with zeros.
Add or subtract as with whole numbers, keeping the decimal point in the same position in the answer.

Example (Addition): 12.5 + 6.37
   12.50
+   6.37
─────
   18.87

Example (Subtraction): 20.00 − 7.45 = 12.55

5. Key Points to Remember

Trailing zeros after the last digit after the decimal point do not change the value: 2.50 = 2.5.
Leading zeros before the first significant digit matter: 0.05 ≠ 0.5.
To convert a fraction with denominator 10 or 100 to decimal: e.g., 3/10 = 0.3, 27/100 = 0.27.
A decimal number is between two consecutive whole numbers. e.g., 4.7 is between 4 and 5.
Every fraction can be written as a decimal and every decimal as a fraction.

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