Class 10 Decimal Expansions — practice questions with answers
Number Systems · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
1. A rational number qp (in lowest terms) has a terminating decimal expansion only when q can be written in the form:
A2n×5m
B2n×3m
C3n×5m
Dany prime power
Show answer
Answer: A) 2n×5m
A rational number qp in lowest terms terminates exactly when the denominator q has only 2 and 5 as prime factors, i.e. q=2n×5m.
2. After how many places of decimal will the number 23×5217 terminate?
A2
B3
C4
D6
Show answer
Answer: B) 3
Denominator 23×52; max(3,2) = 3, so it terminates after 3 decimal places. (20017=0.085.)
3. Is 22×54×71 a terminating decimal?
ANo, the factor 7 makes it recurring
BYes, it terminates
CIt is irrational
DOnly if numerator is even
Show answer
Answer: A) No, the factor 7 makes it recurring
Although 2 and 5 are present, the prime 7 in the denominator (in lowest terms) means the expansion is non-terminating recurring.
4. Two students convert recurring decimals to fractions. Student A says 0.4444...=94. Student B says 0.7777...=97. Which, if any, are correct?
ABoth are correct
BOnly A is correct
COnly B is correct
DNeither is correct
Show answer
Answer: A) Both are correct
For a single repeating digit d, 0.ddd...=9d. So 0.4444...=94 and 0.7777...=97. Both correct.
5. Look at the bar graph. It shows the fraction of a job each of three machines completes: A = 83, B = 41, C = 83. Which machine's fraction, when written as a decimal, has the MOST digits after the decimal point?
AA (0.375)
BB (0.25)
CC only differs from A
DAll have the same number of digits
Show answer
Answer: A) A (0.375)
A = 83=0.375 (denominator 2³, 3 places). B = 41=0.25 (2 places). C = 83=0.375 (3 places). A and C both have 3 places, more than B; among the listed options, A (0.375) is the correct choice.