Decimal Fractions

decimal fractions

Step by Step solutions of Concise Mathematics ICSE Class-7 Maths chapter 4- Decimal Fractions by Selina is provided.

Table Of Contents
  1. Q1: Convert the following into fractions in their lowest terms:
  2. Q2: Convert into decimal fractions:
  3. Q3: Write the number of decimal places in:
  4. Q4: Write the following decimals as word statements:
  5. Q5: Convert the given fractions into like fractions:
  6. Q1: Add:
  7. Q2: Subtract the first number from the second:
  8. Q3: Simplify:
  9. Q4: Find the difference between 6.85 and 0.685.
  10. Q5: Take out the sum of 19.38 and 56.025 from 200.111.
  11. Q6: Add 13.95 and 1.003, and from the result, subtract the sum of 2.794 and 6.2.
  12. Q7: What should be added to 39.587 to give 80.375?
  13. Q8: What should be subtracted from 100 to give 19.29?
  14. Q9: What is excess of 584.29 over 213.95?
  15. Q10: Evaluate:
  16. Q11: What is the excess of 75 over 48.29?
  17. Q12: If A = 237.98 and B = 83.47. Find:
  18. Q13: The cost of one kg of sugar increases from ₹28.47 to ₹32.65. Find the increase in cost.
  19. Q1: Multiply:
  20. Q2: Multiply each number by 10, 100 and 1000:
  21. Q3: Evaluate:
  22. Q4: Divide:
  23. Q5: Divide each of given numbers by 10, 100, 1000 and 10000:
  24. Q6: Evaluate:
  25. Q7: Evaluate:
  26. Q8: Evaluate:
  27. Q9: Find the cost of 36.75 kg wheat at rate of ₹12.80 per kg.
  28. Q10: The cost of a pen is ₹56.15. Find the cost of 16 such pens.
  29. Q11: Evaluate
  30. Q12: Fifteen identical articles weigh 31.50 kg. Find the weigh of each article.
  31. Q13: The product of two numbers is 211.2. If one of these two numbers is 16.5, find the other number.
  32. Q14: One dozen identical articles cost ₹45.96. Find the cost of each article.
  33. Q15: Find whether the given division forms a terminating or a non-terminating decimal:
  34. Q1: The weight of an object is 306 kg. Find the total weight of 48 similar objects.
  35. Q2: Find the cost of 17.5m cloth at the rate of ₹112.50 per metre.
  36. Q3: One kilogram of oil costs ₹73.40. Find the cost of ₹9.75 kilograms of the oil.
  37. Q4: Total weight of 8 identical objects is 51.2 kg. Find the weight of each object.
  38. Q5: 18.5 m of oil costs ₹ 666. Find the cost of 3.8 m cloth.
  39. Q6: Find the value of:
  40. Q7: Evaluate:
  41. Q1: Which is greater: 5.038 or 5.3?
  42. Q2: Shyama bought 5 kg 300 g apples and 3 kg 250 g mangoes. Saria bought 4 kg 800 g oranges and 4 kg 150 g bananas. Who bought more fruits?
  43. Q3: Two kg of milk contains 0.315 kg of cream. The cream in 20 kg milk is:
  44. Q4: The distance walked by a boy is 86.4 km in 4.8 hours. The distance covered by him in one hour is:
  45. Q5: The number seven and 7 thousandth is:
  46. Q6: \(56.56\div1.4\) is equal to:
  47. Q7: \(\left(2+\frac{1}{2}\right)\div\frac{3}{5}\) is equal to:
  48. Q8: Total cost of two pens at ₹5.30 each and four notebooks at ₹20.50 each is:
  49. Q9: \(2.5+3.8\div0.02\) is equal to:
  50. Q10: By what decimal number should 0.0001 be divided to get 0.01?
  51. Q11: \(3\frac{1}{5}\times\left(\frac{1}{2}+\frac{3}{8}\right)\div\frac{21}{40}\) is equal to:
  52. Q12: 5.80, 0.95, 1.87 and 1.92 in descending order are:
  53. Q13: \(3-\frac{1}{4}\ of\ \left(15.8-3\right)\) is equal to:
  54. Q14: Statement 1: \(0.05=0.050=0.005=0.00500\) Statement 2: Any number of zeros put at the end (i.e. on the right side) of a decimal number does not change its value. Which of the following options is correct?
  55. Q15: Assertion (A): Representation of 6.25 as a vulgar fraction is \(6\frac{1}{4}\). Reason (R): A fraction is said to be a vulgar fraction if the denominator is a whole number but not of the form \({10}^n,\ n\in N\).
  56. Q16: Assertion (A): If the product of two decimal numbers is 17.55 and one of them is 6.5, then other one is 2.7. Reason (R): In division of decimal numbers, the dividend is always exactly divisible and no remainder is left after certain steps. Also quotient is always reduced to a terminating decimal.
  57. Q17: Assertion (A): \(3.10\div\left(0.1\times0.1\right)=3.1\). Reason (R): In division of a decimal number by \({10}^n,\ n\in N\), shift the decimal point to the right by as many digits equivalent to n in the power of 10 in the divisor.
  58. Q18: Assertion (A): 9, 9.56, 9.2, 9.005 are all unlike decimals, hence addition operations can't be performed. Reason (R): A whole number can also be expressed as a decimal number by putting a decimal after its unit's digit and after it as many zeroes required to perform addition operations with other like or unlike decimal numbers.

Exercise: 4-B

Q1: Add:

i. 0.5 and 0.37

  0.50
+ 0.37
───────
  0.87

Answer: 0.87

ii. 3.8 and 8.7

  3.8
+ 8.7
──────
 12.5

Answer: 12.5

iii. 0.02, 0.008 and 0.309

  0.020
+ 0.008
+ 0.309
────────
  0.337

Answer: 0.337

iv. 0.4136, 0.3195 and 0.52

  0.4136
+ 0.3195
+ 0.5200
─────────
  1.2531

Answer: 1.2531

v. 9.25, 3.4 and 6.666

  9.250
+ 3.400
+ 6.666
────────
 19.316

Answer: 19.316

vi. 3.007, 0.587 and 18.341

  3.007
+ 0.587
+18.341
────────
 21.935

Answer: 21.935

vii. 0.2, 0.02 and 2.0002

  0.2000
+ 0.0200
+ 2.0002
─────────
  2.2202

Answer: 2.2202

viii. 6.08, 60.8, 0.608 and 0.0608

  6.0800
+60.8000
+ 0.6080
+ 0.0608
──────────
 67.5488

Answer: 67.5488

ix. 29.03, 0.0003, 0.3 and 7.2

 29.0300
+ 0.0003
+ 0.3000
+ 7.2000
──────────
 36.5303

Answer: 36.5303

x. 3.4, 2.025, 9.36 and 3.6221

  3.4000
+ 2.0250
+ 9.3600
+ 3.6221
──────────
 18.4071

Answer: 18.4071

Q2: Subtract the first number from the second:

i. Subtract 5.4 from 9.8

  9.8
− 5.4
 ─────
  4.4

Answer: 4.4

ii. Subtract 0.16 from 4.3

  4.30
− 0.16
──────
  4.14

Answer: 4.14

iii. Subtract 0.82 from 8.6

  8.60
− 0.82
──────
  7.78

Answer: 7.78

iv. Subtract 0.07 from 8.43

  8.43
− 0.07
──────
  8.36

Answer: 8.36

v. Subtract 2.237 from 9.425

  9.425
− 2.237
───────
  7.188

Answer: 7.188

vi. Subtract 41.03 from 59.46

 59.46
−41.03
──────
 18.43

Answer: 18.43

vii. Subtract 3.92 from 26.86

 26.86
− 3.92
──────
 22.94

Answer: 22.94

viii. Subtract 4.73 from 8.5

 8.50
−4.73
─────
 3.77

Answer: 3.77

ix. Subtract 12.63 from 36.2

 36.20
−12.63
──────
 23.57

Answer: 23.57

x. Subtract 0.845 from 3.71

 3.710
−0.845
──────
 2.865

Answer: 2.865

Q3: Simplify:

i. \(28.796 – 13.42 – 2.555\)

Step 1: Add 13.42 and 2.555

 13.420
+ 2.555
───────
 15.975

Step 2: Subtract result from 28.796

 28.796
−15.975
───────
 12.821

Answer: 12.821

ii. \(93.354 – 62.82 – 13.045\)

Step 1: Add 62.82 and 13.045

 62.820
+13.045
───────
 75.865

Step 2: Subtract result from 93.354

 93.354
−75.865
───────
 17.489

Answer: 17.489

iii. \(36 – 18.59 – 3.2\)

Step 1: Add 18.59 and 3.2

 18.590
+ 3.200
───────
 21.790

Step 2: Subtract result from 36

 36.000
−21.790
───────
 14.210

Answer: 14.210

iv. \(86 + 16.95 – 3.0042\)

Step 1: Add 86 and 16.95

 86.0000
+16.9500
────────
102.9500

Step 2: Subtract 3.0042 from result

102.9500
− 3.0042
────────
 99.9458

Answer: 99.9458

v. \(32.8 – 13 – 10.725 + 3.517\)

Step 1: Add 13 and 10.725

 13.000
+10.725
───────
 23.725

Step 2: Add 32.8 and 3.517

 32.800
+ 3.517
───────
 36.317

Step 3: Subtract 23.725 from 36.317

 36.317
−23.725
───────
 12.592

Answer: 12.592

vi. \(4000 – 30.51 – 753.101 – 69.43\)

Step 1: Add 30.51, 753.101, and 69.43

  30.510
+753.101
+ 69.430
─────────
 853.041

Step 2: Subtract 853.041 from 4000

4000.000
−853.041
────────
3146.959

Answer: 3146.959

vii. \(0.1835 + 163.2005 – 25.9 – 100\)

Step 1: Add 0.1835 and 163.2005

   0.1835
+163.2005
─────────
 163.3840

Step 2: Add 25.9 and 100

  25.900
+100.000
────────
 125.900

Step 3: Subtract 125.9 from 163.384

 163.384
−125.900
────────
  37.484

Answer: 37.484

viii. \(38.00 – 30 + 200.200 – 0.230\)

Step 1: Add 38.00 and 200.200

 38.000
+200.200
────────
238.200

Step 2: Add 30 and 0.230

 30.000
+ 0.230
────────
 30.230

Step 3: Subtract 30.230 from 238.200

238.200
−30.230
────────
207.970

Answer: 207.970

ix. \(555.555 + 55.555 – 5.55 – 0.555\)

Step 1: Add 555.555 and 55.555

555.555
+55.555
───────
611.110

Step 2: Add 5.55 and 0.555

 5.550
+0.555
──────
 6.105

Step 3: Subtract 6.105 from 611.110

611.110
− 6.105
───────
605.005

Answer: 605.005

Q4: Find the difference between 6.85 and 0.685.

Step 1: Write the numbers aligning the decimal points.

 6.850
-0.685
 ──────

Step 2: Subtract the digits starting from the right.

  6.850
- 0.685
 ──────
  6.165

Answer: The difference is 6.165.

Q5: Take out the sum of 19.38 and 56.025 from 200.111.

Step 1: Find the sum of 19.38 and 56.025. Align decimals and add:

  19.380
+ 56.025
 ───────
  75.405

Step 2: Subtract the sum (75.405) from 200.111. Align decimals and subtract:

200.111
-75.405
────────
124.706

Answer: The result is 124.706.

Q6: Add 13.95 and 1.003, and from the result, subtract the sum of 2.794 and 6.2.

Step 1: Add 13.95 and 1.003. Align decimals and add:

13.950
+1.003
───────
14.953

Step 2: Add 2.794 and 6.2. Align decimals and add:

 2.794
+6.200
───────
 8.994

Step 3: Subtract the sum (8.994) from the first result (14.953):

14.953
-8.994
───────
 5.959

Answer: The final result is 5.959.

Q7: What should be added to 39.587 to give 80.375?

Step 1: Let the number to be added be \( x \). Then, \[ 39.587 + x = 80.375 \]Step 2: Rearrange to find \( x \): \[ x = 80.375 – 39.587 \]Step 3: Subtract \( 39.587 \) from \( 80.375 \):

  80.375
- 39.587
 ───────
  40.788

Answer: The number to be added is 40.788.

Q8: What should be subtracted from 100 to give 19.29?

Step 1: Let the number to be subtracted be \( x \). Then, \[ 100 – x = 19.29 \]Step 2: Rearrange to find \( x \): \[ x = 100 – 19.29 \]Step 3: Subtract \( 19.29 \) from \( 100 \):

100.00
-19.29
───────
 80.71

Answer: The number to be subtracted is 80.71.

Q9: What is excess of 584.29 over 213.95?

Step 1: Excess means the difference between the two numbers, i.e., subtract the smaller number from the larger number. \[ \text{Excess} = 584.29 – 213.95 \]Step 2: Perform the subtraction:

  584.29
- 213.95
 ───────
  370.34

Answer: The excess of 584.29 over 213.95 is 370.34.

Q10: Evaluate:

i. \(\left(5.4 – 0.8\right) + \left(2.97 – 1.462\right)\)

Step 1: Calculate \(5.4 – 0.8\):

  5.4
- 0.8
 ────
  4.6

Step 2: Calculate \(2.97 – 1.462\):

  2.970
- 1.462
 ──────
  1.508

Step 3: Add the two results:

  4.6
+ 1.508
 ──────
  6.108

Answer: \(6.108\)

ii. \(\left(6.25 + 0.36\right) – \left(17.2 – 8.97\right)\)

Step 1: Calculate \(6.25 + 0.36\):

  6.25
+ 0.36
 ─────
  6.61

Step 2: Calculate \(17.2 – 8.97\):

 17.20
- 8.97
 ─────
  8.23

Step 3: Subtract the second result from the first:

  6.61
- 8.23
 ─────
 -1.62

Answer: \(-1.62\)

iii. \(9.004 + \left(3 – 2.462\right)\)

Step 1: Calculate \(3 – 2.462\):

  3.000
- 2.462
  ─────
  0.538

Step 2: Add the result to \(9.004\):

  9.004
+ 0.538
  ─────
  9.542

Answer: \(9.542\)

iv. \(879.4 – \left(87.94 – 8.794\right)\)

Step 1: Calculate \(87.94 – 8.794\):

87.940
-8.794
──────
79.146

Step 2: Subtract the result from \(879.4\):

879.400
-79.146
───────
800.254

Answer: \(800.254\)

Q11: What is the excess of 75 over 48.29?

Step 1: Write the expression for excess: \[ \text{Excess} = 75 – 48.29 \]Step 2: Subtract 48.29 from 75:

   75.00
 - 48.29
  ───────
   26.71

Answer: \(26.71\)

Q12: If A = 237.98 and B = 83.47. Find:

i. \( A – B \)

Step 1: Write the subtraction expression: \[ A – B = 237.98 – 83.47 \]Step 2: Perform the subtraction:

 237.98
- 83.47
───────
 154.51

Answer: \(154.51\)

ii. \( B – A \)

Step 1: Write the subtraction expression: \[ B – A = 83.47 – 237.98 \]Step 2: Perform the subtraction (result will be negative):

  83.47
-237.98
───────
-154.51

Answer: \(-154.51\)

Q13: The cost of one kg of sugar increases from ₹28.47 to ₹32.65. Find the increase in cost.

Step 1: Write the expression for increase in cost: \[ \text{Increase} = 32.65 – 28.47 \]Step 2: Subtract the original cost from the new cost:

  32.65
- 28.47
───────
   4.18

Answer: ₹4.18

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