Converting Fractions to Decimals (Grade 4)
Fractions and decimals are two different ways of representing parts of a whole. Converting fractions to decimals means writing a fraction in decimal form. This skill is essential for comparing, adding, and working with both forms.
In Class 4, you will learn to convert fractions with denominators of 10 and 100 to decimals, and convert common fractions like 1/2, 1/4, and 3/4 to decimal form.
What is Converting Fractions to Decimals - Class 4 Maths (Decimals)?
To convert a fraction to a decimal:
- If the denominator is 10: place the numerator in the tenths position. Example: 7/10 = 0.7.
- If the denominator is 100: place the numerator in the tenths and hundredths positions. Example: 35/100 = 0.35.
- For other fractions: make the denominator 10 or 100 using equivalent fractions, or divide the numerator by the denominator.
Fraction → Decimal: Divide numerator by denominator
Types and Properties
Common Fraction-Decimal Conversions:
| Fraction | Equivalent | Decimal |
|---|---|---|
| 1/2 | 5/10 | 0.5 |
| 1/4 | 25/100 | 0.25 |
| 3/4 | 75/100 | 0.75 |
| 1/5 | 2/10 | 0.2 |
| 2/5 | 4/10 | 0.4 |
| 3/5 | 6/10 | 0.6 |
| 1/10 | 1/10 | 0.1 |
| 1/20 | 5/100 | 0.05 |
Solved Examples
Example 1: Example 1: Fraction with Denominator 10
Problem: Convert 3/10 to a decimal.
Solution:
Step 1: Denominator is 10, so place numerator in the tenths position.
Answer: 3/10 = 0.3
Example 2: Example 2: Fraction with Denominator 100
Problem: Convert 47/100 to a decimal.
Solution:
Step 1: Denominator is 100, so the numerator spans tenths and hundredths.
Step 2: 47/100 = 0.47.
Answer: 47/100 = 0.47
Example 3: Example 3: Convert 1/2 to a Decimal
Problem: Convert 1/2 to a decimal.
Solution:
Method 1: Make denominator 10. Multiply top and bottom by 5: 1/2 = 5/10 = 0.5.
Method 2: Divide: 1 ÷ 2 = 0.5.
Answer: 1/2 = 0.5
Example 4: Example 4: Convert 1/4 to a Decimal
Problem: Convert 1/4 to a decimal.
Solution:
Step 1: Make denominator 100. Multiply by 25: 1/4 = 25/100 = 0.25.
Answer: 1/4 = 0.25
Example 5: Example 5: Convert 3/4 to a Decimal
Problem: Convert 3/4 to a decimal.
Solution:
Step 1: Make denominator 100. Multiply by 25: 3/4 = 75/100 = 0.75.
Answer: 3/4 = 0.75
Example 6: Example 6: Convert 2/5 to a Decimal
Problem: Convert 2/5 to a decimal.
Solution:
Step 1: Make denominator 10. Multiply by 2: 2/5 = 4/10 = 0.4.
Answer: 2/5 = 0.4
Example 7: Example 7: Convert a Mixed Number
Problem: Convert 2 3/10 to a decimal.
Solution:
Step 1: Whole part = 2. Fraction = 3/10 = 0.3.
Step 2: Combine: 2 + 0.3 = 2.3.
Answer: 2 3/10 = 2.3
Example 8: Example 8: Convert Decimal to Fraction
Problem: Convert 0.65 to a fraction in simplest form.
Solution:
Step 1: 0.65 = 65/100.
Step 2: Simplify: HCF(65, 100) = 5. So 65÷5 / 100÷5 = 13/20.
Answer: 0.65 = 13/20
Example 9: Example 9: Word Problem
Problem: Kavi drank 1/4 of a litre of milk. Neha drank 0.3 litres. Who drank more?
Solution:
Step 1: Convert 1/4 to decimal: 1/4 = 0.25.
Step 2: Compare: 0.25 and 0.30. Since 0.30 > 0.25.
Answer: Neha drank more (0.3 litres > 0.25 litres).
Key Points to Remember
- To convert a fraction to a decimal, divide the numerator by the denominator or make the denominator 10 or 100.
- Fractions with denominator 10: numerator goes in the tenths place.
- Fractions with denominator 100: numerator goes in the tenths and hundredths places.
- Key conversions: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2.
- To convert decimal to fraction: write the decimal as a fraction over 10 or 100 and simplify.
- Converting helps in comparing fractions and decimals easily.
Practice Problems
- Convert 9/10 to a decimal.
- Convert 3/100 to a decimal.
- Convert 4/5 to a decimal.
- Convert 0.45 to a fraction in simplest form.
- Convert 3 1/4 to a decimal.
- Which is greater: 3/4 or 0.7? Convert and compare.
- Aman has Rs.3.50 and Ria has 3 1/2 rupees. Do they have the same amount?
Frequently Asked Questions
Q1. How do you convert a fraction to a decimal?
Divide the numerator by the denominator. Or, if you can make the denominator 10 or 100 using equivalent fractions, place the numerator in the right decimal positions.
Q2. What is 1/2 as a decimal?
1/2 = 0.5. You can get this by dividing 1 by 2, or by converting 1/2 to 5/10.
Q3. What is 1/4 as a decimal?
1/4 = 0.25. Convert by making the denominator 100: 1/4 = 25/100 = 0.25.
Q4. How do you convert a decimal to a fraction?
Count the decimal places. For 1 place, use denominator 10. For 2 places, use 100. Write the digits as the numerator and simplify. Example: 0.35 = 35/100 = 7/20.
Q5. Can all fractions be converted to exact decimals?
Not all. Fractions like 1/3 give repeating decimals (0.333...). In Class 4, you mainly work with fractions that give exact (terminating) decimals, like 1/2, 1/4, 1/5, and 1/10.
Q6. Why is converting between fractions and decimals useful?
It helps in comparing values (is 3/4 more or less than 0.8?), working with money, and solving real-life problems where one form may be easier than the other.
Q7. What is 3/5 as a decimal?
3/5 = 6/10 = 0.6. Multiply both numerator and denominator by 2 to get a denominator of 10.
Q8. How do you convert a mixed number to a decimal?
Convert only the fraction part to a decimal and add it to the whole number. For example, 2 1/4 = 2 + 0.25 = 2.25.
Q9. Is this topic in the NCERT Class 4 syllabus?
Yes. Converting between fractions and decimals is part of the Decimals chapter in Class 4 NCERT Maths. Students learn to convert fractions with denominators 10 and 100, and common fractions like 1/2 and 1/4.
