Class 8 Maths Chapter 10 Decimal Forms Questions and Answers Kerala Syllabus

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SCERT Class 8 Maths Chapter 10 Solutions Decimal Forms

Class 8 Kerala Syllabus Maths Solutions Chapter 10 Decimal Forms Questions and Answers

Decimal Forms Class 8 Questions and Answers Kerala Syllabus

Earlier Forms (Page 164)

Question 1.
Write in fractional form, the numbers given in decimal form below:
(i) 0.1
(ii) 0.01
(iii) 0.11
(iv) 0.101
(v) 0.0101
Answer:
(i) 0.1 = \(\frac {1}{10}\)
(ii) 0.01 = \(\frac {1}{100}\)
(iii) 0.11 = \(\frac {11}{100}\)
(iv) 0.101 = \(\frac {101}{1000}\)
(v) 0.0101 = \(\frac {101}{10000}\)

Some Other Fractions (Page 166)

Question 1.
Write the fractions below in decimal form:
(i) \(\frac {3}{20}\)
(ii) \(\frac {3}{40}\)
(iii) \(\frac {13}{40}\)
(iv) \(\frac {7}{80}\)
(v) \(\frac {5}{16}\)
Answer:
(i) \(\frac{3}{20}=\frac{3 \times 5}{20 \times 5}=\frac{15}{100}\) = 0.15

(ii) 40 = 2 × 2 × (2 × 5)
Multiplied by 5 × 5
(2 × 5) × (2 × 5) × (2 × 5) = 1000
It is a multiple of 10.
\(\frac{3}{40}=\frac{3 \times 5 \times 5}{40 \times 5 \times 5}=\frac{75}{1000}\) = 0.075

(iii) 40 = 2 × 2 × (2 × 5)
Multiplied by 5 × 5
(2 × 5) × (2 × 5) × (2 × 5) = 1000
It is a multiple of 10.
\(\frac{13}{40}=\frac{13 \times 5 \times 5}{40 \times 5 \times 5}=\frac{325}{1000}\) = 0.325

(iv) 80 = 2 × 2 × 2 × (2 × 5)
Multiplied by 5 × 5 × 5
(2 × 5) × (2 × 5) × (2 × 5) × (2 × 5) = 10000
It is a multiple of 10.
\(\frac{7}{80}=\frac{7 \times 5 \times 5 \times 5}{80 \times 5 \times 5 \times 5}=\frac{875}{10000}\) = 0.0875

(v) 16 = 2 × 2 × 2 × 2
Multiplied by 5 × 5 × 5 × 5
(2 × 5) × (2 × 5) × (2 × 5) × (2 × 5) = 10000
It is a multiple of 10.
\(\frac{5}{16}=\frac{5 \times 5 \times 5 \times 5 \times 5}{16 \times 5 \times 5 \times 5 \times 5}=\frac{3125}{10000}\) = 0.3125

Question 2.
Find the decimal form of the sums below:
(i) \(\frac{1}{5}+\frac{1}{25}+\frac{1}{125}\)
(ii) \(\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}+\frac{1}{5^4}\)
(iii) \(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}\)
Answer:

Question 3.
A two-digit number divided by another two-digit number gives 5.875. What are the numbers?
Answer:
5.875 = \(\frac {5875}{1000}\)
5875 = 5 × 5 × 5 × 47
1000 = 5 × 5 × 5 × 8

5.875 = \(\frac{5875}{1000}=\frac{5 \times 5 \times 5 \times 47}{5 \times 5 \times 5 \times 8}=\frac{47}{8}\)
But 8 is not a two-digit number.
So we multiplied both numerator and denominator by 2, and we get
\(\frac{47}{8}=\frac{94}{16}\)
5.875 = \(\frac {94}{16}\)

New forms (Page 172)

Question 1.
Find fractions with powers of 10 as denominators that get closer and closer to each of the fractions below, and write the decimal form of each:
(i) \(\frac {5}{6}\)
(ii) \(\frac {1}{9}\)
(iii) \(\frac {1}{11}\)
Answer:

Question 2.
Prove that the numbers \(\frac{1}{10}, \frac{11}{100}, \frac{111}{1000}, \ldots\) get closer and closer to \(\frac {1}{9}\).
(ii) Find the decimal forms of \(\frac{1}{9}, \frac{2}{9}, \frac{3}{9}, \frac{4}{9}, \frac{5}{9}, \frac{6}{9}, \frac{7}{9}, \frac{8}{9}\)
(iii) What are the decimal forms of \(\frac {2}{3}\)?
Answer:

Question 3.
Compute the following and write answers in decimal form:
(i) 0.111… + 0.222…
(ii) 0.333… + 0.777…
(iii) 0.333… × 0.666…
Answer:
(i) 0.111 = \(\frac {1}{9}\)

Question 4.
For each of the fractions below, write the decimal form of a fraction with a difference less than \(\frac {1}{1000}\)
(i) \(\frac {1}{3}\)
(ii) \(\frac {1}{6}\)
(iii) \(\frac {2}{3}\)
(iv) \(\frac {5}{6}\)
(v) \(\frac {1}{7}\)
Answer:
(i) \(\frac {1}{3}\) = 0.333
(ii) \(\frac {1}{6}\) = 0.166 (or 0.167)
(iii) \(\frac {2}{3}\) = 0.666 (or 0.667)
(iv) \(\frac {5}{6}\) = 0.833
(v) \(\frac {1}{7}\) = 0.142

Class 8 Maths Chapter 10 Kerala Syllabus Decimal Forms Questions and Answers

Class 8 Maths Decimal Forms Questions and Answers

Question 1.
What is the decimal form of the fraction \(\frac {1}{8}\)?
(A) 0.18
(B) 0.125
(C) 0.8
(D) 0.0125
Answer:
(B) 0.125

Question 2.
Which of the following fractions has the decimal form 0.04?
(A) \(\frac {1}{4}\)
(B) \(\frac {4}{10}\)
(C) \(\frac {1}{25}\)
(D) \(\frac {2}{5}\)
Answer:
(C) \(\frac {1}{25}\)

Question 3.
Read the given statements.
Statement I: The fraction \(\frac {1}{3}\) cannot be written as a fraction with a denominator that is a power of 10 (like 10, 100, 1000).
Statement II: The decimal form of \(\frac {1}{3}\) is the recurring decimal 0.333….
Choose the correct answer:
(A) Statement I is true, and Statement II is false.
(B) Statement I is false, and Statement II is true.
(C) Both statements are true.
(D) Both statements are false.
Answer:
(C) Both statements are true

Question 4.
Read the given statements.
Statement I: 0.03 = \(\frac {3}{100}\)
Statement II: 0.03 can be split as \(\frac {0}{10}\) + \(\frac {3}{100}\).
Choose the correct answer:
(A) Statement I is true, and Statement II is false.
(B) Statement I is false, and Statement II is true.
(C) Both statements are true, and II explains I.
(D) Both statements are false.
Answer:
(C) Both statements are true, and II explains I.

Question 5.
If \(\frac {1}{9}\) = 0.111…, then what is the decimal form of \(\frac {5}{9}\)?
(A) 0.5
(B) 0.0505…
(C) 0.555…
(D) 0.9595…
Answer:
(C) 0.555…

Question 6.
What is the missing number in the expansion of 0.72?
0.72 = \(\frac{7}{10}+\frac{\cdots .}{100}\)
(A) 7
(B) 2
(C) 72
(D) 0
Answer:
(B) 2

Question 7.
Write in decimals
(a) \(\frac {1}{9}\)
(b) \(\frac {2}{9}\)
(c) \(\frac {1}{7}\)
(d) \(\frac {1}{11}\)
(e) \(\frac {2}{11}\)
(f) \(\frac {1}{12}\)
Answer:
(a) 0.111…
(b) 0.222…
(c) 0.14285…
(d) 0.090909…
(e) 0.181818…
(f) 0.08333…

Question 8.
Find the fraction of the denominator that is a power of 10 equal to each of the fractions below, and then write their decimal forms:
(i) \(\frac {1}{50}\)
(ii) \(\frac {3}{40}\)
(iii) \(\frac {5}{16}\)
(iv) \(\frac {12}{625}\)
Answer:

Question 9.
Find the fraction of the denominator that is a power of 10, getting closer and closer to each of the fractions below, and then write their decimal forms.
(i) \(\frac {5}{6}\)
(ii) \(\frac {3}{11}\)
(iii) \(\frac {23}{11}\)
(iv) \(\frac {1}{13}\)
Answer:

Question 10.
(i) Explain using algebra that the fractions \(\frac{1}{10}, \frac{11}{100}, \frac{111}{1000}, \ldots\) get closer and closer to \(\frac {1}{9}\).
(ii) Using the general principle above on single digit numbers, find the decimal forms of \(\frac{2}{9}, \frac{4}{9}, \frac{5}{9}, \frac{7}{9}, \frac{8}{9}\) (Why \(\frac {3}{9}\) and \(\frac {6}{9}\) left out in this?)
(iii) What can we say in general about those decimal forms in which a single digit repeats?
Answer:
(i) Let x be the number
\(\frac{x}{9}-\frac{x}{10}=\frac{x}{90}=\frac{x}{9}-\frac{11 x}{100}=\frac{x}{900}\)



(\(\frac {3}{9}\), \(\frac {6}{9}\). These fractions having common factor in the numerator and the denominator.
(iii) Repeated decimals.

Question 11.
(a) Find the decimal form of \(\frac {1}{4}\).
(b) Write the decimal form of \(\frac{7}{10}+\frac{3}{100}+\frac{4}{1000}\).
Answer:

Question 12.
(a) Write the decimal forms of \(\frac {1}{3}\) and \(\frac {1}{9}\).
(b) What is the decimal form of (0.33333….)²?
Answer:

Question 13.
Write the decimal forms of \(\frac {3}{25}\) and \(\frac {1}{8}\).
Answer:
\(\frac{3}{25}=\frac{3 \times 4}{25 \times 4}=\frac{12}{100}\) = 0.12
\(\frac{1}{8}=\frac{1 \times 125}{8 \times 125}=\frac{125}{1000}\) = 0.125

Question 14.
(a) Write the decimal form of the fractions \(\frac {1}{2}\) and \(\frac {2}{5}\).
(b) If \(\frac {4}{k}\) is a fraction between \(\frac {1}{2}\) and \(\frac {2}{5}\). What is k?
(c) Write the decimal form of the fraction \(\frac {4}{k}\).
Answer:

If \(\frac {4}{k}\) is between \(\frac {1}{2}\) and \(\frac {2}{5}\), then \(\frac {4}{k}\) is between \(\frac {4}{8}\) and \(\frac {4}{10}\).
Then the number is \(\frac {4}{9}\)
∴ k = 9
(c) \(\frac {4}{9}\) = 0.444…

Question 15.
(i) Find the decimal form of \(\frac {1}{11}\).
(ii) Find the decimal forms of \(\frac {2}{11}\), \(\frac {3}{11}\).
(iii) What is the decimal form of \(\frac {10}{11}\)?
Answer:

Question 16.
Write the results of the operations below as decimals:
(i) (0.333….)²
(ii) \(\sqrt{0.444 \ldots \ldots}\)
Answer:

Question 17.
Write the decimal form of \(\frac {1}{6}\)
Answer:
\(\frac {1}{6}\) = 0.1666…..

Class 8 Maths Chapter 10 Notes Kerala Syllabus Decimal Forms

Fractions with Powers of 10 as Denominators
Fractions with powers of 10 as denominators can be written in decimal form.
\(\frac {3}{10}\) = 0.3
\(\frac {54}{10}\) = 5.4
\(\frac {29}{100}\) = 0.29
\(\frac {54}{100}\) = 0.54
\(\frac {347}{1000}\) = 0.347
\(\frac {54}{1000}\) = 0.054

Any number in decimal form can be written using fractions with powers of 10 as denominators.
0.7 = \(\frac {7}{10}\)
0.91 = \(\frac {91}{100}\)
0.673 = \(\frac {673}{1000}\)

Decimal numbers can be splitted according to place value.

Some Other Fractions
Convention of some fractions, whose denominators are not powers of 10.

New forms
Conversion of some fractions, whose denominators were not powers of 10.