Decimal Fraction— Concepts, Formulas & Shortcuts
- Multiplying decimals: multiply as whole numbers, then place the point after (sum of decimal places) digits.
- Dividing decimals: shift the point in both numbers until the divisor is a whole number.
- 0.5 = 1/2, 0.25 = 1/4, 0.75 = 3/4, 0.125 = 1/8, 0.2 = 1/5, 0.375 = 3/8.
- Pure recurring decimal: 0.abab… = ab/99; 0.3̄ = 3/9 = 1/3.
- Comparing decimals: pad with zeros so all have the same number of decimal places, then compare as integers.
- Annexing zeros to the right of a decimal never changes its value: 0.7 = 0.70 = 0.700.
Decimal Fraction Practice Questions with Answers
Attempt each question first, then open the explanation. All 21 questions below are free to read and require no signup.
Q1.0.75 expressed as a fraction in lowest terms is:
Easy- A3/4
- B7/5
- C15/2
- D75/10
Decimal Fraction question 1 of 21+Show Answer & Explanation
Answer: A. 3/4
Explanation: 0.75 = 75/100 = 3/4.
Q2.The value of 0.0025 × 400 is:
Moderate- A0.1
- B1
- C10
- D100
Decimal Fraction question 2 of 21+Show Answer & Explanation
Answer: B. 1
Explanation: 25 × 400 = 10,000; with 4 decimal places restored, the answer is 1.0000 = 1.
Q3.3/8 written as a decimal is:
Easy- A0.325
- B0.375
- C0.38
- D0.83
Decimal Fraction question 3 of 21+Show Answer & Explanation
Answer: B. 0.375
Explanation: Divide the numerator by the denominator: 3 ÷ 8 = 0.375.
Q4.The recurring decimal 0.3̄ equals:
Moderate- A3/10
- B1/3
- C3/99
- D33/100
Decimal Fraction question 4 of 21+Show Answer & Explanation
Answer: B. 1/3
Explanation: A single repeating digit goes over 9: 3/9 = 1/3.
Q5.The value of 1.2 × 0.5 is:
Easy- A0.06
- B0.6
- C6
- D0.12
Decimal Fraction question 5 of 21+Show Answer & Explanation
Answer: B. 0.6
Explanation: 12 × 5 = 60; two decimal places give 0.60 = 0.6.
Q6.Which of these is the largest?
Easy- A0.7
- B0.07
- C0.707
- D0.77
Decimal Fraction question 6 of 21+Show Answer & Explanation
Answer: D. 0.77
Explanation: Padding to three places: 0.700, 0.070, 0.707, 0.770 → 0.77 is the largest.
Q7.The value of 0.5 ÷ 0.05 is:
Easy- A0.1
- B1
- C10
- D100
Decimal Fraction question 7 of 21+Show Answer & Explanation
Answer: C. 10
Explanation: Shift both points two places: 50 ÷ 5 = 10.
Q8.0.25 expressed as a fraction in lowest terms is:
Easy- A1/2
- B1/4
- C1/5
- D2/5
Decimal Fraction question 8 of 21+Show Answer & Explanation
Answer: B. 1/4
Explanation: 0.25 = 25/100 = 1/4.
Q9.The value of 0.3 × 0.3 is:
Easy- A0.009
- B0.09
- C0.9
- D9
Decimal Fraction question 9 of 21+Show Answer & Explanation
Answer: B. 0.09
Explanation: 3 × 3 = 9, and two decimal places give 0.09.
Q10.The value of 2.5 ÷ 0.5 is:
Easy- A0.5
- B5
- C50
- D500
Decimal Fraction question 10 of 21+Show Answer & Explanation
Answer: B. 5
Explanation: Shift both decimal points one place: 25 ÷ 5 = 5.
Q11.5/8 written as a decimal is:
Easy- A0.575
- B0.625
- C0.65
- D0.85
Decimal Fraction question 11 of 21+Show Answer & Explanation
Answer: B. 0.625
Explanation: Divide the numerator by the denominator: 5 ÷ 8 = 0.625.
Q12.The recurring decimal 0.6̄ equals:
Moderate- A3/5
- B2/3
- C6/11
- D3/4
Decimal Fraction question 12 of 21+Show Answer & Explanation
Answer: B. 2/3
Explanation: A single repeating digit goes over 9: 6/9 = 2/3.
Q13.Which of these is the smallest?
Easy- A0.4
- B0.04
- C0.44
- D0.404
Decimal Fraction question 13 of 21+Show Answer & Explanation
Answer: B. 0.04
Explanation: Padded to three places: 0.400, 0.040, 0.440, 0.404 → 0.04 is smallest.
Q14.The value of 1.5 × 0.02 is:
Moderate- A0.003
- B0.03
- C0.3
- D3
Decimal Fraction question 14 of 21+Show Answer & Explanation
Answer: B. 0.03
Explanation: 15 × 2 = 30; with three decimal places restored, 0.030 = 0.03.
Q15.0.5 expressed as a fraction is:
Easy- A1/5
- B1/2
- C2/5
- D5/10
Decimal Fraction question 15 of 21+Show Answer & Explanation
Answer: B. 1/2
Explanation: 0.5 = 5/10 = 1/2 in lowest terms.
Q16.The value of 0.2 × 0.4 is:
Easy- A0.008
- B0.08
- C0.8
- D8
Decimal Fraction question 16 of 21+Show Answer & Explanation
Answer: B. 0.08
Explanation: 2 × 4 = 8, and two decimal places give 0.08.
Q17.1/4 written as a decimal is:
Easy- A0.14
- B0.2
- C0.25
- D0.4
Decimal Fraction question 17 of 21+Show Answer & Explanation
Answer: C. 0.25
Explanation: Divide the numerator by the denominator: 1 ÷ 4 = 0.25.
Q18.The value of 4.5 ÷ 0.9 is:
Moderate- A0.5
- B5
- C45
- D50
Decimal Fraction question 18 of 21+Show Answer & Explanation
Answer: B. 5
Explanation: Shift both decimal points one place: 45 ÷ 9 = 5.
Q19.Which of these is the largest?
Easy- A0.3
- B0.33
- C0.303
- D0.033
Decimal Fraction question 19 of 21+Show Answer & Explanation
Answer: B. 0.33
Explanation: Padded to three places: 0.300, 0.330, 0.303, 0.033 → 0.33 is largest.
Q20.The recurring decimal 0.9̄ is equal to:
Difficult- A0.9
- B0.99
- C1
- D9/10
Decimal Fraction question 20 of 21+Show Answer & Explanation
Answer: C. 1
Explanation: A single repeating digit goes over 9: 9/9 = 1.
Q21.The value of 0.06 × 100 is:
Easy- A0.6
- B6
- C60
- D600
Decimal Fraction question 21 of 21+Show Answer & Explanation
Answer: B. 6
Explanation: Multiplying by 100 moves the decimal point two places right: 6.
Decimal Fraction — Frequently Asked Questions
How do I convert a recurring decimal into a fraction?+
For a purely recurring decimal, put the repeating block over as many 9s as it has digits. 0.3̄ = 3/9 = 1/3 and 0.27‾ = 27/99 = 3/11.
How do I compare decimals reliably?+
Give every number the same number of decimal places by adding trailing zeros, then compare them as if they were whole numbers. 0.7 becomes 0.700 and is clearly less than 0.770.
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