Rational to Decimal

Grade 7 · decimals · 82 practice problems · read aloud

🔊 Listen to this explanation

Rational to Decimal Conversion

This operation helps us convert any fraction (a rational number) into its decimal form. It's super useful because decimals are often easier to compare, add, or subtract than fractions. You'll see decimals everywhere—in money, measurements, and data!

How to Convert a Fraction to a Decimal 🧮

  1. Identify your fraction (e.g., 3/4).
  2. Divide the numerator (top number) by the denominator (bottom number). The fraction bar means division!
  3. Set up your division problem. The numerator goes inside the division bracket, and the denominator goes outside.
  4. Divide, adding a decimal point and zeros to the numerator as needed.
  5. Keep dividing until the decimal terminates (ends) or you spot a repeating pattern.

Worked Examples

Example 1: 3/4

3 ÷ 4 = ?
Since 4 is larger than 3, we write 3.0 inside the bracket. 4 goes into 30 seven times (4 x 7 = 28). 30 - 28 = 2. Bring down another 0. 4 goes into 20 five times exactly (4 x 5 = 20). No remainder!
Answer: 0.75 (This is a terminating decimal).

Example 2: 2/3

2 ÷ 3 = ?
Since 3 is larger than 2, we write 2.000 inside the bracket. 3 goes into 20 six times (3 x 6 = 18). 20 - 18 = 2. This remainder of 2 keeps repeating, causing the 6 to repeat forever.
Answer: 0.666... or 0.6 (This is a repeating decimal).

⚠️ Common Mistakes to Avoid

  • Dividing backwards: Always divide the numerator by the denominator (top ÷ bottom), not the other way around!
  • Misplacing the decimal: Be careful when you bring down the decimal point into your answer. Line it up directly above its position in the dividend.
  • Forgetting repeating decimals: If you get the same remainder over and over, you've found a repeating decimal. Don't just stop—show the pattern with a bar over the repeating digits.

🌟 Tips & Tricks

  • Memory Aid: Think "Top Dog in the House!" The numerator (top number) goes inside the division house.
  • Shortcut: If the denominator is 10, 100, 1000, etc., just move the decimal point in the numerator to the left based on the number of zeros (e.g., 23/100 = 0.23).
  • Know your common conversions: 1/2 = 0.5, 1/4 = 0.25, 1/3 ≈ 0.3, 1/5 = 0.2.

How to Practice

To master this skill, try these activities:

  • Create a set of flashcards with fractions on one side and their decimal equivalents on the other.
  • Ask a friend or parent to give you five fractions to convert. Time yourself for an extra challenge!
  • Look for fractions in real life (recipes, rulers) and practice converting them to decimals in your head.

Practice problems

6 of the 82, worked through step by step — try them before opening the answer.

1 0.75 + 1/4 = ?

Hint: Convert the fraction to a decimal or the decimal to a fraction so both numbers are in the same form before adding.

Show the answer

Answer: 1

  1. Understand the problem. We are adding a decimal (0.75) and a fraction (1/4). To add them easily, we should write both in the same form — either both as decimals or both as fractions.
  2. Convert 1/4 to a decimal. We know 1 divided by 4 is 0.25. So, 1/4 = 0.25.
  3. Add the decimals. 0.75 + 0.25 = 1.00.
  4. Check by converting both to fractions. 0.75 = 75/100 = 3/4. So 0.75 + 1/4 = 3/4 + 1/4 = 4/4 = 1.
  5. Conclusion. Both methods give the same result: 1. ANSWER: 1

Let's solve 0.75 + 1/4 step by step.

2 3.75 ÷ 0.25 = ?

Hint: When dividing by a decimal, you can multiply both numbers by the same power of 10 to eliminate the decimal in the divisor. For example, 1.2 ÷ 0.3 becomes 12 ÷ 3.

Show the answer

Answer: 15

  1. Understand the problem. We are dividing 3.75 by 0.25. Division by a decimal can be tricky, so we can make it easier by eliminating the decimals.
  2. Multiply both the dividend (3.75) and the divisor (0.25) by the same number so that the divisor becomes a whole number. Here, the divisor 0.25 has two decimal places. If we multiply it by 100, it becomes 25. So multiply both numbers by 100: 3.75 × 100 = 375 0.25 × 100 = 25
  3. Now the problem becomes: 375 ÷ 25
  4. Perform the division. How many times does 25 go into 375? 25 × 10 = 250 375 − 250 = 125 25 × 5 = 125 125 − 125 = 0 So 25 goes into 375 exactly 10 + 5 = 15 times.
  5. Conclusion. 375 ÷ 25 = 15 Therefore, 3.75 ÷ 0.25 = 15. Final answer: 15

Let's solve 3.75 ÷ 0.25 step-by-step.

3 0.75 × 1.2 ÷ 0.5 = ?

Hint: When working with decimal multiplication and division, consider converting to fractions or working step-by-step with the operations in order.

Show the answer

Answer: 1.8

  1. Write the problem clearly. 0.75 × 1.2 ÷ 0.5
  2. Multiplication and division have the same priority, so we go left to right. First, multiply 0.75 × 1.2. 0.75 × 1.2 = 0.75 × (12/10) = (75/100) × (12/10) = (75 × 12) / (100 × 10) = 900 / 1000 = 0.9 So after the first step: 0.9 ÷ 0.5
  3. Now divide 0.9 ÷ 0.5. 0.9 ÷ 0.5 = 0.9 / 0.5 = (9/10) / (5/10) = (9/10) × (10/5) = 9/5 = 1.8
  4. Final answer. 0.75 × 1.2 ÷ 0.5 = 1.8

Let's solve step by step.

4 0.75 × 2.4 ÷ 0.3 = ?

Hint: When working with decimal multiplication and division, consider converting the decimals to fractions to simplify the calculation. For example, 0.5 × 1.2 ÷ 0.2 can be approached by thinking of 0.5 as 1/2, 1.2 as 6/5, and 0.2 as 1/5.

Show the answer

Answer: 6

  1. Write the problem as given. 0.75 × 2.4 ÷ 0.3
  2. Multiplication and division have the same priority, so we go left to right. First, multiply 0.75 × 2.4. 0.75 × 2.4 = 0.75 × (24/10) = (75/100) × (24/10) = (3/4) × (24/10) = (3 × 24) / (4 × 10) = (72) / (40) = 72 ÷ 40 = 1.8 So, 0.75 × 2.4 = 1.8.
  3. Now divide the result by 0.3. 1.8 ÷ 0.3 = 1.8 / 0.3 Multiply numerator and denominator by 10 to remove decimal: (1.8 × 10) / (0.3 × 10) = 18 / 3 = 6.
  4. Final answer. 0.75 × 2.4 ÷ 0.3 = 6. Answer: 6

Let's solve step by step.

5 0.75 × 2.4 ÷ 0.6 = ?

Hint: When working with decimal multiplication and division, consider converting the decimals to fractions to make the operations easier. For example, 0.5 × 1.2 ÷ 0.3 would become 1/2 × 6/5 ÷ 3/10.

Show the answer

Answer: 3

  1. Convert decimals to fractions for clarity** 0.75 = 75/100 = 3/4 2.4 = 24/10 = 12/5 0.6 = 6/10 = 3/5 So the problem becomes: (3/4) × (12/5) ÷ (3/5) --- **
  2. Understand division by a fraction** Dividing by (3/5) is the same as multiplying by its reciprocal (5/3). So: (3/4) × (12/5) × (5/3) --- **
  3. Multiply the fractions** Multiply numerators: 3 × 12 × 5 = 180 Multiply denominators: 4 × 5 × 3 = 60 So we have: 180/60 --- **
  4. Simplify** 180 ÷ 60 = 3 --- **
  5. Conclusion**

Let's solve step by step. We have: 0.75 × 2.4 ÷ 0.6 --- ** The answer is 3.

6 (3/4 + 1/2) × 0.8 = ?

Hint: First convert all terms to the same format, then follow the order of operations.

Show the answer

Answer: 1

  1. Simplify inside the parentheses: 3/4 + 1/2 First, find a common denominator for 3/4 and 1/2. The common denominator is 4. 1/2 = 2/4. So 3/4 + 2/4 = 5/4.
  2. Now we have (5/4) × 0.8. Convert 0.8 to a fraction: 0.8 = 8/10 = 4/5.
  3. Multiply the fractions: (5/4) × (4/5) Multiply numerators: 5 × 4 = 20 Multiply denominators: 4 × 5 = 20 So 20/20 = 1.
  4. Conclusion (3/4 + 1/2) × 0.8 = 1.

Let's solve step-by-step.

Practise this topic — 10 free problems, no signup →