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Vidaara.orgClass 10 · Mathematics
CodeVID-M10-01-DEC-01
Decimal Expansions of Rationals — Assignment
Chapter: Number Systems
Topic: Decimal Expansions of Rational Numbers
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
$\tfrac{p}{q}$ (lowest terms) terminates iff $q$ has the form:
  • A.$2^m5^n$
  • B.$2^m3^n$
  • C.$3^m5^n$
  • D.any
2.
$\tfrac18$ is:
  • A.terminating
  • B.non-terminating
  • C.irrational
  • D.zero
3.
$\tfrac17$ is:
  • A.terminating
  • B.non-terminating repeating
  • C.irrational
  • D.an integer
4.
$\tfrac{7}{20}$ is:
  • A.terminating
  • B.non-terminating
  • C.irrational
  • D.zero
5.
$\tfrac{11}{12}$ is:
  • A.terminating
  • B.non-terminating repeating
  • C.irrational
  • D.an integer
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Without dividing, state whether $\tfrac{13}{8}$ terminates.
7.
Does $\tfrac{17}{30}$ terminate?
8.
State the decimal type of $\tfrac{23}{2^3\cdot5^2}$.
9.
Is $\tfrac{64}{455}$ terminating?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
State (with reason) whether $\tfrac{6}{15}$ has a terminating decimal.
11.
Express $\tfrac38$ as a decimal.
12.
After how many places does $\tfrac{13}{2^2\cdot5^3}$ terminate?
13.
Is $\tfrac{29}{343}$ terminating?
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Without dividing, state whether each terminates: $\tfrac{13}{3125},\ \tfrac{17}{8},\ \tfrac{64}{455},\ \tfrac{15}{1600}$.
15.
Write the decimal expansions of $\tfrac{17}{8}$ and $\tfrac{13}{3125}$.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $2^m5^n$
  2. (A) terminating
  3. (B) non-terminating repeating
  4. (A) terminating
  5. (B) non-terminating repeating
Section B — Short Answer (2 marks)
  1. Terminating ($8=2^3$).
  2. No ($30=2\cdot3\cdot5$ has a factor $3$).
  3. Terminating.
  4. No ($455=5\cdot7\cdot13$).
Section C — Short Answer (3 marks)
  1. $\tfrac{6}{15}=\tfrac25$ — terminating.
  2. $0.375$.
  3. $3$ places.
  4. No ($343=7^3$).
Section D — Long Answer (5 marks)
  1. Terminating, terminating, non-terminating, terminating (respectively).
  2. $2.125$ and $0.00416$.
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