Express 0.25 as a fraction in its lowest terms.

14. 0.25 = 25100, and dividing numerator and denominator by 25 gives 14.

60. Multiply top and bottom by 1000: 0.480.008 = 4808 = 60.

Which of these is the largest number: 0.7, 0.71, 0.0709, 0.717?

0.717. Compare digit by digit after the point. 0.717 has 7 tenths, 1 hundredth and 7 thousandths, which exceeds 0.710 and 0.700; 0.0709 has only 0 tenths.

Find the value of 0. 6 + 0. 7 + 0. 8.

2. 3. Each single-digit recurring decimal is that digit over 9: 69 + 79 + 89 = 219 = 73 = 2. 3.

If 1440.144 = 14.4x, find x.

0.0144. 1440.144 = 1000, so 14.4x = 1000, which gives x = 14.41000 = 0.0144.

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Quantitative Aptitude · Numbers & Simplification

Decimal Fractions — Questions & Answers

Decimal fraction questions ask you to convert between fractions and decimals, compare and order decimals, and compute with them quickly. Recurring decimals convert to fractions with a standard trick.

5 solved questions
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Key formulas

To divide by a decimal, shift the point in both numbers: $\dfrac{0.36}{0.04} = \dfrac{36}{4} = 9$
Pure recurring: $0.\overline{ab} = \dfrac{ab}{99}$ ; e.g. $0.\overline{27} = \dfrac{27}{99} = \dfrac{3}{11}$
Mixed recurring: $0.a\overline{b} = \dfrac{ab - a}{90}$

5 solved Decimal Fractions questions

Try each question first — tap an option to check your answer, or open Learn step by step for a guided walkthrough.

01
Express 0.25 as a fraction in its lowest terms.
5 steps · reveal one at a time
1. Step 1: Understand the decimal
  The number $0.25$ has two decimal places. The last digit, $5$ , is in the hundredths place. This means $0.25$ can be read as "twenty-five hundredths".
2. Step 2: Convert to fraction
  To convert $0.25$ to a fraction, we can write the number after the decimal point as the numerator and use $100$ as the denominator. So, $0.25 = \frac{25}{100}$ .
3. Step 3: Simplify the fraction
  Now we need to simplify the fraction $\frac{25}{100}$ to its lowest terms. Find the greatest common divisor (GCD) of $25$ and $100$ . Both numbers are divisible by $25$ .
4. Step 4: Divide by GCD
  Divide both the numerator and the denominator by $25$ : $\frac{25 \div 25}{100 \div 25} = \frac{1}{4}$ . This fraction is now in its lowest terms as $1$ and $4$ share no common factors other than $1$ .
5. Step 5: The answer
  So the answer is (A) $\dfrac{1}{4}$ . The decimal $0.25$ is equivalent to the fraction $\dfrac{1}{4}$ when expressed in its simplest form.
02
Evaluate $\dfrac{0.48}{0.008}$ .
5 steps · reveal one at a time
1. Step 1: Understand the problem
  We need to evaluate the expression $\dfrac{0.48}{0.008}$ . Dividing decimals can be challenging, so our first goal is to convert this into a division of whole numbers.
2. Step 2: Remove decimals
  To eliminate the decimals, we multiply both the numerator and the denominator by the same power of 10. This keeps the value of the fraction unchanged.
3. Step 3: Find the multiplier
  Look at the denominator, $0.008$ . It has three decimal places. To make it a whole number, we need to multiply it by $1000$ . We must also multiply the numerator by $1000$ .
4. Step 4: Simplify the fraction
  Multiplying both parts by $1000$ gives us: $\dfrac{0.48 \times 1000}{0.008 \times 1000} = \dfrac{480}{8}$ . This is a much simpler division.
5. Step 5: The answer
  Now, perform the division: $480 \div 8 = 60$ . So the answer is (C) 60, which is the result of the simplified division.
03
Which of these is the largest number: 0.7, 0.71, 0.0709, 0.717?
5 steps · reveal one at a time
1. Step 1: Align Decimals
  To compare decimal numbers, it's helpful to align them and add trailing zeros so they all have the same number of decimal places. This makes comparison easier. We can write the numbers as: $0.7000$ , $0.7100$ , $0.0709$ , $0.7170$ .
2. Step 2: Compare Tenths Digit
  Now, let's compare the first digit after the decimal point (the tenths place). We have $0.7$ , $0.7$ , $0.0$ , and $0.7$ . The number $0.0709$ has a $0$ in the tenths place, making it smaller than the others, which all have $7$ .
3. Step 3: Compare Hundredths Digit
  Next, compare the numbers that have $7$ in the tenths place: $0.7000$ , $0.7100$ , and $0.7170$ . Look at the hundredths digit. We have $0$ , $1$ , and $1$ . The number $0.7000$ has $0$ in the hundredths place, making it smaller than $0.7100$ and $0.7170$ .
4. Step 4: Compare Thousandths Digit
  Finally, we compare $0.7100$ and $0.7170$ . Both have $7$ in the tenths place and $1$ in the hundredths place. Now look at the thousandths digit. $0.7100$ has $0$ , while $0.7170$ has $7$ . Since $7$ is greater than $0$ , $0.7170$ is the largest number.
5. Step 5: The answer
  So the answer is (D) 0.717. This number has $7$ tenths, $1$ hundredth, and $7$ thousandths, which is greater than all other options when compared digit by digit.
04
Find the value of $0.\overline{6} + 0.\overline{7} + 0.\overline{8}$ .
5 steps · reveal one at a time
1. Step 1: Convert to fractions
  Remember that a single-digit recurring decimal, like $0.\overline{d}$ , can be written as the fraction $d/9$ . We will apply this rule to each term in the sum to convert them into fractions.
2. Step 2: Rewrite the sum
  Using the conversion rule, we can rewrite the expression as a sum of fractions: $0.\overline{6} + 0.\overline{7} + 0.\overline{8} = 6/9 + 7/9 + 8/9$ . Now, we can add these fractions.
3. Step 3: Add the fractions
  Since all fractions have the same denominator, we simply add their numerators: $(6+7+8)/9 = 21/9$ . This gives us a single fraction representing the sum.
4. Step 4: Simplify and convert
  The fraction $21/9$ can be simplified by dividing both numerator and denominator by 3, resulting in $7/3$ . Converting $7/3$ back to a decimal gives $2.\overline{3}$ .
5. Step 5: The answer
  So the answer is (A) $2.\overline{3}$ , because the sum of the recurring decimals simplifies to $7/3$ , which is $2.\overline{3}$ .
05
If $\dfrac{144}{0.144} = \dfrac{14.4}{x}$ , find $x$ .
5 steps · reveal one at a time
1. Step 1: Simplify the fraction
  First, let's simplify the left side of the equation, $\dfrac{144}{0.144}$ . Notice that $144$ is $1000$ times $0.144$ . Therefore, $\dfrac{144}{0.144} = 1000$ .
2. Step 2: Form the equation
  Now that we know the left side equals $1000$ , we can substitute this back into the original equation. This gives us the simpler equation: $1000 = \dfrac{14.4}{x}$ .
3. Step 3: Isolate x
  To find $x$ , we need to isolate it. We can rearrange the equation by multiplying both sides by $x$ , which gives $1000x = 14.4$ . Then, divide both sides by $1000$ to solve for $x$ .
4. Step 4: Calculate x
  Dividing $14.4$ by $1000$ means moving the decimal point three places to the left. So, $x = \dfrac{14.4}{1000} = 0.0144$ . This is our final value for $x$ .
5. Step 5: The answer
  So the answer is (B) 0.0144. This value correctly satisfies the original equation.

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