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: (56.56div1.4) is equal to:
  47. Q7: (left(2+frac{1}{2}right)divfrac{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+3.8div0.02) is equal to:
  50. Q10: By what decimal number should 0.0001 be divided to get 0.01?
  51. Q11: (3frac{1}{5}timesleft(frac{1}{2}+frac{3}{8}right)divfrac{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(15.8-3right)) 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 (6frac{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, nin 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): (3.10divleft(0.1times0.1right)=3.1). Reason (R): In division of a decimal number by ({10}^n, nin 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-A

Q1: Convert the following into fractions in their lowest terms:

i. 3.75

Step 1: Write the decimal as a fraction. \[ 3.75 = \frac{375}{100} \] Step 2: Reduce to lowest terms. \[ \frac{375 \div 25}{100 \div 25} = \frac{15}{4} \] Answer: \(\frac{15}{4}\)

ii. 0.5

Step 1: Write as a fraction. \[ 0.5 = \frac{5}{10} \] Step 2: Reduce to lowest terms. \[ \frac{5 \div 5}{10 \div 5} = \frac{1}{2} \] Answer: \(\frac{1}{2}\)

iii. 2.04

Step 1: Write as a fraction. \[ 2.04 = \frac{204}{100} \] Step 2: Reduce to lowest terms. \[ \frac{204 \div 4}{100 \div 4} = \frac{51}{25} \] Answer: \(\frac{51}{25}\)

iv. 0.65

Step 1: Write as a fraction. \[ 0.65 = \frac{65}{100} \] Step 2: Reduce to lowest terms. \[ \frac{65 \div 5}{100 \div 5} = \frac{13}{20} \] Answer: \(\frac{13}{20}\)

v. 2.405

Step 1: Write as a fraction. \[ 2.405 = \frac{2405}{1000} \] Step 2: Reduce to lowest terms. \[ \frac{2405 \div 5}{1000 \div 5} = \frac{481}{200} \] Answer: \(\frac{481}{200}\)

vi. 0.085

Step 1: Write as a fraction. \[ 0.085 = \frac{85}{1000} \] Step 2: Reduce to lowest terms. \[ \frac{85 \div 5}{1000 \div 5} = \frac{17}{200} \] Answer: \(\frac{17}{200}\)

vii. 8.025

Step 1: Write as a fraction. \[ 8.025 = \frac{8025}{1000} \] Step 2: Reduce to lowest terms. \[ \frac{8025 \div 25}{1000 \div 25} = \frac{321}{40} \] Answer: \(\frac{321}{40}\)

Q2: Convert into decimal fractions:

i. \(2\frac{4}{5}\)

Step 1: Convert to improper fraction: \[ 2\frac{4}{5} = \frac{(2 \times 5) + 4}{5} = \frac{14}{5} \] Step 2: Divide numerator by denominator: \[ \frac{14}{5} = 2.8 \] Answer: 2.8

ii. \(\frac{79}{100}\)

Step 1: Divide numerator by denominator: \[ \frac{79}{100} = 0.79 \] Answer: 0.79

iii. \(\frac{37}{10,000}\)

Step 1: Divide numerator by denominator: \[ \frac{37}{10000} = 0.0037 \] Answer: 0.0037

iv. \(\frac{7543}{{10}^4}\)

Step 1: \({10}^4 = 10000\) \[ \frac{7543}{10000} = 0.7543 \] Answer: 0.7543

v. \(\frac{3}{4}\)

Step 1: Divide numerator by denominator: \[ \frac{3}{4} = 0.75 \] Answer: 0.75

vi. \(9\frac{3}{5}\)

Step 1: Convert to improper fraction: \[ 9\frac{3}{5} = \frac{(9 \times 5) + 3}{5} = \frac{48}{5} \] Step 2: Divide numerator by denominator: \[ \frac{48}{5} = 9.6 \] Answer: 9.6

vii. \(8\frac{5}{8}\)

Step 1: Convert to improper fraction: \[ 8\frac{5}{8} = \frac{(8 \times 8) + 5}{8} = \frac{69}{8} \] Step 2: Divide numerator by denominator: \[ \frac{69}{8} = 8.625 \] Answer: 8.625

viii. \(5\frac{7}{8}\)

Step 1: Convert to improper fraction: \[ 5\frac{7}{8} = \frac{(5 \times 8) + 7}{8} = \frac{47}{8} \] Step 2: Divide numerator by denominator: \[ \frac{47}{8} = 5.875 \] Answer: 5.875

Q3: Write the number of decimal places in:

i. \(0.4762\)

Step 1: Count digits after the decimal point. \[ \text{Digits after decimal in } 0.4762 = 4 \] Answer: 4 decimal places

ii. \(7.00349\)

Step 1: Count digits after the decimal point. \[ \text{Digits after decimal in } 7.00349 = 5 \] Answer: 5 decimal places

iii. \(8235.403\)

Step 1: Count digits after the decimal point. \[ \text{Digits after decimal in } 8235.403 = 3 \] Answer: 3 decimal places

iv. \(35.4\)

Step 1: Count digits after the decimal point. \[ \text{Digits after decimal in } 35.4 = 1 \] Answer: 1 decimal place

v. \(2.608\)

Step 1: Count digits after the decimal point. \[ \text{Digits after decimal in } 2.608 = 3 \] Answer: 3 decimal places

vi. \(0.000879\)

Step 1: Count digits after the decimal point. \[ \text{Digits after decimal in } 0.000879 = 6 \] Answer: 6 decimal places

Q4: Write the following decimals as word statements:

i. \(0.4, 0.9, 0.1\)

Step 1: Express each decimal as “zero-point-” followed by digits read individually.

  • \(0.4\) — zero-point-four
  • \(0.9\) — zero-point-nine
  • \(0.1\) — zero-point-one

Answer: zero-point-four, zero-point-nine, zero-point-one

ii. \(1.9, 4.4, 7.5\)

Step 1: Read the whole number, then say “point” followed by digits individually.

  • \(1.9\) — one-point-nine
  • \(4.4\) — four-point-four
  • \(7.5\) — seven-point-five

Answer: one-point-nine, four-point-four, seven-point-five

iii. \(0.02, 0.56, 13.06\)

Step 1: Read as zero-point- for decimals less than 1 and whole number with point for others.

  • \(0.02\) — zero-point-zero-two
  • \(0.56\) — zero-point-five-six
  • \(13.06\) — thirteen-point-zero-six

Answer: zero-point-zero-two, zero-point-five-six, thirteen-point-zero-six

iv. \(0.005, 0.207, 111.519\)

Step 1: Read digit-by-digit after decimal, starting with zero-point- for decimals less than 1.

  • \(0.005\) — zero-point-zero-zero-five
  • \(0.207\) — zero-point-two-zero-seven
  • \(111.519\) — one hundred eleven-point-five-one-nine

Answer: zero-point-zero-zero-five, zero-point-two-zero-seven, one hundred eleven-point-five-one-nine

v. \(0.8, 0.08, 0.008, 0.0008\)

Step 1: Use zero-point- and read every digit after decimal individually.

  • \(0.8\) — zero-point-eight
  • \(0.08\) — zero-point-zero-eight
  • \(0.008\) — zero-point-zero-zero-eight
  • \(0.0008\) — zero-point-zero-zero-zero-eight

Answer: zero-point-eight, zero-point-zero-eight, zero-point-zero-zero-eight, zero-point-zero-zero-zero-eight

vi. \(256.1, 10.22, 0.634\)

Step 1: Read the whole number, then “point” followed by digits individually.

  • \(256.1\) — two hundred fifty-six-point-one
  • \(10.22\) — ten-point-two-two
  • \(0.634\) — zero-point-six-three-four

Answer: two hundred fifty-six-point-one, ten-point-two-two, zero-point-six-three-four

Q5: Convert the given fractions into like fractions:

i. \(0.5, 3.62, 43.981, \text{ and } 232.0037\)

Step 1: Find the decimal with the greatest number of decimal places. \[ 0.5 = 0.5 \quad (\text{1 decimal place}) \\ 3.62 = 3.62 \quad (\text{2 decimal places}) \\ 43.981 = 43.981 \quad (\text{3 decimal places}) \\ 232.0037 = 232.0037 \quad (\text{4 decimal places}) \]Step 2: Convert all decimals to have the same number of decimal places (4 decimal places, as in 232.0037) by adding zeros. \[ 0.5 = 0.5000 \\ 3.62 = 3.6200 \\ 43.981 = 43.9810 \\ 232.0037 = 232.0037 \]Answer: 0.5000, 3.6200, 43.9810, 232.0037

ii. \(215.78, 33.0006, 530.3, \text{ and } 0.03569\)

Step 1: Find the decimal with the greatest number of decimal places. \[ 215.78 = 215.78 \quad (\text{2 decimal places}) \\ 33.0006 = 33.0006 \quad (\text{4 decimal places}) \\ 530.3 = 530.3 \quad (\text{1 decimal place}) \\ 0.03569 = 0.03569 \quad (\text{5 decimal places}) \]Step 2: Convert all decimals to have the same number of decimal places (5 decimal places, as in 0.03569) by adding zeros. \[ 215.78 = 215.78000 \\ 33.0006 = 33.00060 \\ 530.3 = 530.30000 \\ 0.03569 = 0.03569 \\ \]Answer: 215.78000, 33.00060, 530.30000, 0.03569

previous
next

Pages: 1 2 3 4 5

Share the Post:

Leave a Comment

Your email address will not be published. Required fields are marked *

Related Posts​

Join Our Newsletter

Name
Email
The form has been submitted successfully!
There has been some error while submitting the form. Please verify all form fields again.

Start typing and press enter to search

Scroll to Top