Converting Percentage to Decimal
Converting a percentage to a decimal is one of the simplest and most useful mathematical operations. Since percent means 'per hundred', converting to a decimal simply requires dividing by 100 — or equivalently, moving the decimal point 2 places to the left.
This conversion is essential for calculations: finding 15% of ₹800 is much easier as 0.15 × 800 = ₹120.
What is Converting Percentage to Decimal - Class 5 Maths (Percentage)?
To convert a percentage to a decimal, divide the percentage by 100 (move the decimal point 2 places to the left).
x% = x ÷ 100
Examples:
- 50% = 50 ÷ 100 = 0.50 = 0.5
- 7% = 7 ÷ 100 = 0.07
- 125% = 125 ÷ 100 = 1.25
Converting Percentage to Decimal Formula
Percentage → Decimal: Move the decimal point 2 places LEFT and remove the % sign
| Percentage | Decimal |
|---|---|
| 100% | 1.00 |
| 50% | 0.50 |
| 25% | 0.25 |
| 10% | 0.10 |
| 1% | 0.01 |
| 0.5% | 0.005 |
Solved Examples
Example 1: Example 1: Convert 45% to a decimal
Problem: Convert 45% to a decimal.
Solution:
Move decimal 2 places left: 45% → 0.45
Answer: 45% = 0.45
Example 2: Example 2: Convert 8% to a decimal
Problem: Convert 8% to a decimal.
Solution:
8% = 08% → move 2 places left → 0.08
Answer: 8% = 0.08
Example 3: Example 3: Convert 150% to a decimal
Problem: Convert 150% to a decimal.
Solution:
Move decimal 2 places left: 150% → 1.50 = 1.5
Answer: 150% = 1.5
Example 4: Example 4: Convert 2.5% to a decimal
Problem: Convert 2.5% to a decimal.
Solution:
Move decimal 2 places left: 2.5% → 0.025
Answer: 2.5% = 0.025
Example 5: Example 5: Convert 0.5% to a decimal
Problem: Convert 0.5% to a decimal.
Solution:
Move decimal 2 places left: 0.5% → 0.005
Answer: 0.5% = 0.005
Example 6: Example 6: Using the conversion for calculation
Problem: Find 15% of ₹600.
Solution:
Step 1: Convert 15% to decimal: 15% = 0.15
Step 2: Calculate: 0.15 × 600 = 90
Answer: 15% of ₹600 = ₹90
Example 7: Example 7: Word problem — Marks
Problem: Arjun scored 72% in English. Express this as a decimal and find his marks out of 50.
Solution:
Step 1: 72% = 0.72
Step 2: Marks = 0.72 × 50 = 36
Answer: Arjun scored 36 out of 50.
Example 8: Example 8: Reverse — Decimal to percentage
Problem: Convert 0.35 to a percentage.
Solution:
Move decimal 2 places right: 0.35 → 35%
Answer: 0.35 = 35%
Example 9: Example 9: Converting 100% and 0%
Problem: Convert 100% and 0% to decimals.
Solution:
100% = 100 ÷ 100 = 1.00 (the whole)
0% = 0 ÷ 100 = 0.00 (nothing)
Key Points to Remember
- To convert percentage to decimal: divide by 100 (move decimal 2 places left).
- To convert decimal to percentage: multiply by 100 (move decimal 2 places right).
- Percentages less than 10% give decimals with leading zeroes (8% = 0.08).
- Percentages greater than 100% give decimals greater than 1 (150% = 1.5).
- 100% = 1.0, 50% = 0.5, 25% = 0.25, 10% = 0.1, 1% = 0.01.
- Converting to decimals is useful for multiplication: x% of N = (x/100) × N.
Practice Problems
- Convert 68% to a decimal.
- Convert 3% to a decimal.
- Convert 225% to a decimal.
- Convert 0.25% to a decimal.
- Find 20% of 450 by first converting to a decimal.
- Convert 0.8 to a percentage.
- Neha scored 92% in Maths. Express as a decimal and find her marks out of 75.
- Arrange in order: 45%, 0.5, 3/8.
Frequently Asked Questions
Q1. How do I convert a percentage to a decimal?
Divide the percentage by 100, which is the same as moving the decimal point 2 places to the left. For example, 35% = 0.35 and 7% = 0.07.
Q2. How do I convert a decimal back to a percentage?
Multiply the decimal by 100, which is the same as moving the decimal point 2 places to the right. For example, 0.42 = 42% and 1.5 = 150%.
Q3. Why is this conversion useful?
Converting percentages to decimals makes calculations easier. To find 18% of 250, it is simpler to calculate 0.18 × 250 = 45 than to work with the percentage directly.
Q4. What is 1% as a decimal?
1% = 1 ÷ 100 = 0.01. This means 1 percent is one hundredth. It is a very small portion of the whole.
Q5. Can a percentage be less than 1%?
Yes. For example, 0.5% = 0.005 as a decimal. This represents 5 thousandths, or half of one percent.
Q6. What is the relationship between fractions, decimals, and percentages?
They are three ways to express the same value. 1/4 = 0.25 = 25%. You can convert between any two forms. Percentage ÷ 100 = decimal. Decimal × 100 = percentage.
Q7. How do I compare percentages and decimals?
Convert them to the same form. To compare 35% and 0.4: convert 35% to 0.35. Since 0.35 < 0.4, we know 35% < 0.4 (or 40%).
Q8. Is 200% as a decimal equal to 2?
Yes. 200% = 200 ÷ 100 = 2.0. This means twice the original amount. If an investment grows by 200%, it triples in value (original + 200% of original).
