## Chapter 1 Simplification Decimal Fraction Examples

**Question 1. Express the following numbers in decimal fractions:**

**1. 2 + \(\frac{3}{10}\) **

**Class 6 West Bengal Board Math Solution :**

2 + \(\frac{3}{10}\) = 2 + 0.3

= 2.3

Class 6 West Bengal Board Math Solution

**2. 10 + 7 + \(\frac{8}{1000}\)**

**Solution:**

10 + 7 + \(\frac{8}{1000}\)

= 17 +.008

= 17.008

**3. 6 one-tenths**

**Solution:**

6 one-tenths 0.6

Wbbse Class 6 Maths Solutions

**4. 9 one-hundredths**

**Solution:**

9 one-hundreths =0.09

**Read And Learn More: WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Solved Problems**

**5. Four one-thousandths**

**Class 6 West Bengal Board Math Solution:**

Four one-thousandths = 0.004

**6. Two hundred three decimal four five**

**Solution:**

Two hundred three decimal four five = 203.45

**7. Four thousand two units five one-thousandths **

**Class 6 West Bengal Board Math Solution:**

Four thousand two units five one-thousandth = 4002.005

**8. 400 + 50 + \(\frac{9}{100}\) + \(\frac{1}{1000}\)**

**Solution:**

400 + 50 + \(\frac{9}{100}\) + \(\frac{1}{1000}\)

= 450 +0.09 + 0·001 = 450.091

**9. Two lac two units four 100 1000 one-thousandths**

**Solution:**

Two lac two units four one-thousandths = 20002.004

**10. Six hundred twenty-nine decimal zero five. **

**Class 6 West Bengal Board Math Solution :**

Six hundred twenty-nine decimal zero five = 629.005

**Question 2. Put the following decimal numbers in the respective places of the place value table and then express them in words:**

**1. 27.9**

**2. 1.28**

**3. 65.134**

**4. 42.009**

**5. 38.205**

**6. 4003.08**

**7. 712.5**

**8. 45.06**

**Solution:**

**Expression in Words:**

1. 27.9 = Twenty-seven decimal nine or Twenty-seven nine one-tenths.

2. 128 = One unit two one-tenths eight one-hundred.

3. 65.134 = Sixty-five one one-tenths three one-hundredths four one-thousandths.

4. 42.009 = Forty-two nine one-thousandths or forty-two decimal zero nine.

5. 38.205 = Thirty-eight two one-tenths five one-thousandths

6. 4003.08 = Four thousand three eight one-hundredths.

7. 712.5 = Seven hundred twelve five one-tenths.

8. 45.06 = Forty-five six one-hundredths or forty-five decimal zero six.

**Question 3. Complete the following tables:**

**Class 6 West Bengal Board Math Solution:**

**Question 4. Convert the following decimal fractions to vulgar fractions:**

**1. 0.3**

**Solution:**

0.3 = \(\frac{3}{10}\)

**2. 0.039**

**Solution: **

0.039 = \(\frac{39}{1000}\)

**Question 5. Put >, = or < in the blank spaces of the following:**

**1. 5.0 ****0.5**

**Solution:**

The left-hand number is 5.0, and its integral (or whole part) part is 5.

The right-hand number is 0.5, its integral part is 0.

∴ 5.0 0.5.

**2. 72.1 72.10**

**Solution:**

The whole or integral parts of both the left-hand number and right-hand number are the same (each equal to 72) and also in the decimal part both the numbers have the same one-tenths and so both the numbers are equal.

∴ 72.1 72.10.

**3. 68.5 68.52**

**Solution:**

The integral part of both the numbers is the same; in the decimal part both the numbers have the same one-tenths (each equal to 5) but the one-hundredth part of the left-hand number is 0 and in the right-hand number, the one-hundredth part is 2.

So the right-hand number is greater than the left.

∴ 68.5 68.52.

**4. 72.93 729.3**

**Solution:**

The integral part of the left-hand number is 72 and that of the right-hand number is 729.

∴ 72.97 729.3.

**5. 42.6 ****42.600**

**Solution:**

Both numbers have same the same integral part as well as the decimal part.

So the numbers are the same.

∴ 42.6 42.600.

**6. 2.33 3.22**

**Solution:**

The integral part of the left-hand number is 2 and that in the right-hand number is 3.

∴ 2.33 3.22.

**7. 92.4 ****924.00**

**Solution:**

924 = 924.0 = 924.00

∴ 924 924.00.

**8. 10.01 ****10.10**

**Solution:**

Since both the numbers have the same integral parts and the one-tenths of the left-hand number is 0 but the right-hand number is 1.

∴ 10.01 10.10.

**Question 6. Arrange the following numbers in ascending order of magnitude:**

**1. 0.534, 0.52, 5.34, 0.513**

**Class 6 West Bengal Board Math Solution:**

**Given**

0.534, 0.52, 5.34, 0.513

The integral parts of the given numbers are 0, 0, 5, and 0.

∴ 5.34 is the greatest number.

Again,

0.534 = 0.534

0.52 = 0.520

0.513 = 0.513

As, 513 < 520 < 534

∴ 513 < 520 < 534.

So arranging the given numbers in ascending order of magnitude, we get,

0.513, 0.52, 0.534; 5.34.

**2. 0.536, 0.335, 0.3354,. 0.****52.
**

**Solution:**

**Given**

0.536, 0.335, 0.3354,. 0.52

The integral parts of the given numbers are the same, we have,

0.536 = 0.5360

0.335 = 0.3350

0.3354 = 0.3354

0.52 = 0.5200

∴ As, 3350 < 3354 < 5200 < 5360

0.0335 < 0.3354 < 0·5200 < 0.536

or, 0.335 < 0.3354 <0.52 < 0.536

So arranging the given numbers in ascending order of magnitude we get,

0.335, 0.3354, 0.52, 0:536

**Question 7. Arrange the following numbers in descending order of magnitude:**

**1. 13.3, 11.3, 1.33, 2.31; **

**Class 6 West Bengal Board Math Solution
**

13 \cdot 3=13 \cdot 30 \\

11 \cdot 3=11 \cdot 30 \\

1 \cdot 33=1 \cdot 33 \\

2 \cdot 31=2 \cdot 31

\end{array}\right\}\)

The integral parts of the given numbers are

13, 11, 1, 2.

∵ 13 > 11 2 > 1

∴ 13.30 11.30 > 2.31> 1-33

Arranging the numbers in descending order of magnitudes, we get,

13.3, 11.3, 2.31, 1.33.

**2. 3.007, 3.07, 37.30, 7.13**

**Class 6 West Bengal Board Math Solution:**

3 \cdot 007=3 \cdot 007 \\

3 \cdot 07=3.070 \\

37 \cdot 30=37 \cdot 300 \\

7 \cdot 13=7 \cdot 130

\end{array}\right\}\)

3.007, 3.07, 37.30, 7.13

We get, 37.300 > 7.130

The integral parts of the given numbers are

3, 3, 37, 7

∵ 37 > 7 > 3

We get,

∴ 37.300 > 7.130 > 3.070 > 3.007 ( ∵ 3.070> 3.007)

or, 37.30 > 7.13 > 3.07 > 3.007.

So arranging the given numbers in descending order of magnitudes, we get 37.30, 7.13, 3.07, 3.007.

**Wbbse Class 6 Maths Solutions**

**Question 8. ****Expand the following numbers according to the place value of the digits:**

**1. 101.153 **

**Class 6 West Bengal Board Math Solution:**

101-153 = 101 + \(\frac{1}{10}\) + \(\frac{5}{100}\) + \(\frac{3}{1000}\)

= 100 + 1 + \(\frac{1}{10}\) + \(\frac{5}{100}\) + \(\frac{3}{1000}\)

**2. 57.031.**

**Solution:**

57.031 = 57 + \(\frac{3}{100}\) + \(\frac{1}{1000}\)

= 50 + 7 + \(\frac{3}{100}\) + \(\frac{1}{1000}\)

**Wbbse Class 6 Maths Solutions**

**Question 9. Find the values of the following:**

**1. 0.07 + 0.09**

**Class 6 West Bengal Board Math Solution :**

∴ 0.07 + 0.09 = 0.16.

**2.**** 4.11 + 1.6**

**Solution:**

4.11 = 4.11; 1.6 = 1.60

∴ 4.11 + 1.6 = 4.11 + 1.60

= 5.71

**3. 312.61+ 276.72**

**Class 6 West Bengal Board Math Solution:**

**312.61+ 276.72**

∴ 312.61 + 276.72 = 586.33

**Wbbse Class 6 Maths Solutions**

**4. 5 – 0.555**

**Solution:
**

5 = 5.000; 5.000 = 0.555

∴ 5 – 0.555 = 5.000 – 0.555 = 4.445.

**5. 27.56+14.69**

**Class 6 West Bengal Board Math Solution:
**

27.56 + 14.69 = 42.25.

**6. 4.3 +36.4**

**Solution:**

4.3 = 4.3; 3 = 3.0; 6.4 = 6.4

∴ 4.3 + 3 – 6.4 = 4.3 + 3.0 – 6.4 = 0.9.

**7. 3.36 – 4.62 + 2.18**

**Class 6 West Bengal Board Math Solution :**

3.36 4.62 + 2.18 = 3.36+ 2.184.62.

∴ 3.36 = 4.62 + 2.18

= 3.36 + 2.18 – 4.62 = 0.92.

**8. 2.67 – 3.727 + 4.2**

**Class 6 West Bengal Board Math Solution:
**

2.67 – 3.727 + 4.2

∴ 2.67 – 3.727 + 4.2

= 2.670 + 4·200 – 3.727 = 3.143

**Question 10. For an occasion at our house, Father bought rice for 200, pulses for 125.50, and fish for what ****was spent by Father? ****242.50. How much total amount of money**

**Solution :**

Father spent 568.00 as the total amount of money for the occasion.

**Question 11. ****Your exercise book is rectangular in shape and its length is 24.25 cm and its breadth is 10.75 cm. What is the perimeter of your exercise book?**

** Solution: **

The perimeter of the exercise book = 2 (Length + Breadth)

= 2 (24.25 + 10.75) cm (2 x 35.00) cm 70 cm.

∴ The perimeter of the exercise book = is 70 cm.

**Question 12. You had 5. You bought a pen for 3.50. How much money is left with you at present?**

**Solution :**

₹ 5 = ₹ 5.00

∴ 1.50 is left with you at present.

**Question 13. What must be added to 2.75 to get 3?**

**Solution**

Now 3 = 3.00

∴ 0.25 must be added.

**Question 14. Taniya cuts off a length of 8.5 cm of string from a string of length 12.5 cm. What is the length of the string left?**

**Solution:**

The total length of the string = is 12.5 cm.

From it, a length of 8.5 cm is cut off.

∴ The length of the string is still left = 4 cm.

**Question 15. What must be added to 2.172 to get 5?**

**Solution: **

5 = 5.000

∴ 2.828 is to be added.

**Question 16. 2.647 is subtracted from 4.15. How much is to be added to the result of subtraction to get 10?**

**Solution:**

4.15 = 4.150

∴ The result of subtraction = 1.503.

Now we have to find how much is to be added to 1-503 to get 10.

Now 10 = 10.000

∴ 8.497 must be added.

**Question 17. In a long-jump competition, Susmita jumped 179.25 cm and Sagarika jumped 182.88 cm. Who and how much more length did jump? **

**Solution: **Susmita jumped 179.25 cm and Sagarika jumped 182.88 cm.

As 179.25 cm < 182.88 cm, therefore Sagarika jumped more length than Susmita.

∴ Sagarika jumped 3.63 cm more in length than Susmita.

**Question 18. Simplify :**

**1. \(\frac{10 \cdot 573+2 \cdot 227-1 \cdot 8}{2 \cdot 347-4 \cdot 32+12 \cdot 973}\)**

**Solution:**

The given expression = \(\frac{10 \cdot 573+2 \cdot 227-1 \cdot 8}{2 \cdot 347-4 \cdot 32+12 \cdot 973}\)

**2. ****\(\frac{4 \cdot 5-6 \cdot 12+7 \cdot 432-1 \cdot 1}{5 \cdot 234+10 \cdot 2-2 \cdot 33-8 \cdot 392}\)**

**Solution:**

The given expression = \(\frac{4 \cdot 5-6 \cdot 12+7 \cdot 432-1 \cdot 1}{5 \cdot 234+10 \cdot 2-2 \cdot 33-8 \cdot 392}\)

**Question 19. A man gave 0-5 part of his own property to his wife, 0.2 part to his son, and 0.25 part to his daughter. If he had still the property whose value is ₹ 5000. What is the value of the whole property? What is the value of the property of his wife?**

**Solution: **

Let the whole property = 1 unit.

∴ The total part of the property that his wife, son, and daughter got (0.502+0.25) = 0.95 part

∴ The remaining part of the property = (1 – 0.95) = 0.05 part

∴ Value of 0.05 part of the property = ₹ 5000

∴ Value of the whole property = ₹ (5000 ÷ 0.05) = ₹ 100000.

∴ The value of his wife’s property = ₹ 100000 × 0.5 = ₹ 50000

So the value of the whole property = ₹ 100000. and the value of the wife’s property

= ₹ 50,000.