Dividing Decimals by 10, 100 and 1000
Dividing a decimal by 10, 100, or 1000 is the reverse of multiplying. The decimal point moves to the left. This skill is used in unit conversions (cm to m, g to kg, mL to L) and in understanding place value.
When you divide by 10, the decimal shifts 1 place left. By 100, 2 places left. By 1000, 3 places left. If there are not enough digits, add zeroes before the number.
What is Dividing Decimals by 10, 100 and 1000 - Class 5 Maths (Decimals)?
Rule for dividing decimals by powers of 10:
| Divided by | Decimal point moves | Direction |
|---|---|---|
| ÷ 10 | 1 place | ← Left |
| ÷ 100 | 2 places | ← Left |
| ÷ 1000 | 3 places | ← Left |
Dividing Decimals by 10, 100 and 1000 Formula
Decimal ÷ 10 = Shift decimal point 1 place left
Decimal ÷ 100 = Shift decimal point 2 places left
Decimal ÷ 1000 = Shift decimal point 3 places left
Solved Examples
Example 1: Example 1: Divide by 10
Problem: Calculate 45.6 ÷ 10.
Solution:
Move decimal 1 place left: 45.6 → 4.56
Answer: 45.6 ÷ 10 = 4.56
Example 2: Example 2: Divide by 100
Problem: Calculate 345 ÷ 100.
Solution:
Move decimal 2 places left: 345. → 3.45
Answer: 345 ÷ 100 = 3.45
Example 3: Example 3: Divide by 1000
Problem: Calculate 78 ÷ 1000.
Solution:
Move decimal 3 places left: 78. → 0.078 (add a leading zero)
Answer: 78 ÷ 1000 = 0.078
Example 4: Example 4: Decimal ÷ 10
Problem: Calculate 0.5 ÷ 10.
Solution:
Move decimal 1 place left: 0.5 → 0.05
Answer: 0.5 ÷ 10 = 0.05
Example 5: Example 5: Whole number ÷ 1000
Problem: Calculate 5 ÷ 1000.
Solution:
Move decimal 3 places left: 5. → 0.005
Answer: 5 ÷ 1000 = 0.005
Example 6: Example 6: Word problem — Converting cm to m
Problem: A desk is 125 cm long. Express this in metres (1 m = 100 cm).
Solution:
125 ÷ 100 = 1.25
Answer: The desk is 1.25 m long.
Example 7: Example 7: Word problem — Converting g to kg
Problem: A packet of biscuits weighs 375 g. Express in kilograms.
Solution:
375 ÷ 1000 = 0.375
Answer: The packet weighs 0.375 kg.
Example 8: Example 8: Word problem — Sharing money
Problem: ₹567 is shared equally among 100 students for a charity. How much does each student contribute?
Solution:
567 ÷ 100 = 5.67
Answer: Each student contributes ₹5.67.
Example 9: Example 9: Finding the pattern
Problem: Complete the pattern: 4500, 450, 45, ___, ___
Solution:
Each number is the previous ÷ 10:
45 ÷ 10 = 4.5
4.5 ÷ 10 = 0.45
Answer: 4500, 450, 45, 4.5, 0.45
Key Points to Remember
- Dividing by 10 shifts the decimal point 1 place left.
- Dividing by 100 shifts it 2 places left.
- Dividing by 1000 shifts it 3 places left.
- If there are not enough digits to the left, add leading zeroes (e.g., 7 ÷ 100 = 0.07).
- This is the reverse of multiplying by 10, 100, or 1000.
- Useful for conversions: cm to m (÷100), g to kg (÷1000), mL to L (÷1000), m to km (÷1000).
- Dividing by a power of 10 always makes the number smaller.
Practice Problems
- Calculate 89.5 ÷ 10.
- Calculate 234 ÷ 100.
- Calculate 6.7 ÷ 1000.
- Convert 456 cm to metres.
- Convert 2500 g to kilograms.
- Calculate 0.3 ÷ 100.
- Fill in the blank: ___ ÷ 1000 = 0.045.
- Convert 750 mL to litres.
Frequently Asked Questions
Q1. Why does dividing by 10 shift the decimal left?
Dividing by 10 makes each digit 10 times smaller. A digit in the tens place moves to ones, ones moves to tenths, and so on. This is equivalent to moving the decimal one place to the left.
Q2. What happens when I divide a single digit by 1000?
The decimal point shifts 3 places to the left, and leading zeroes are added. For example, 8 ÷ 1000 = 0.008.
Q3. How is this used in unit conversions?
To convert smaller units to larger units, divide by the appropriate power of 10. Examples: cm to m (÷100), g to kg (÷1000), mm to cm (÷10), mL to L (÷1000).
Q4. Is dividing by 100 the same as multiplying by 0.01?
Yes. Dividing by 100 is the same as multiplying by 1/100 = 0.01. Both shift the decimal two places to the left.
Q5. Can I use this rule for dividing by 20 or 500?
Break it into steps. To divide by 20: divide by 10, then by 2. To divide by 500: divide by 1000, then multiply by 2. Or divide by 100, then divide by 5.
Q6. What is the relationship between multiplying and dividing by 10?
They are inverse operations. Multiplying by 10 shifts the decimal right; dividing by 10 shifts it left. If 2.5 × 10 = 25, then 25 ÷ 10 = 2.5.
Q7. How do leading zeroes work?
Leading zeroes are placed before the first non-zero digit after the decimal point to maintain correct place value. In 0.05, the zero in the tenths place is a necessary placeholder. It shows that the 5 is in the hundredths place, not the tenths.
Q8. Is this covered in the NCERT Class 5 syllabus?
Yes. Dividing decimals by 10, 100, and 1000 is part of the Decimals chapter in the NCERT Class 5 Maths curriculum.
Related Topics
- Division of Decimals
- Multiplying Decimals by 10, 100 and 1000
- Decimals (Grade 5)
- Comparing and Ordering Decimals
- Addition of Decimals
- Subtraction of Decimals
- Multiplication of Decimals
- Converting Fractions to Decimals (Grade 5)
- Converting Decimals to Fractions
- Decimal Word Problems (Grade 5)
- Decimal Place Value (Grade 5)
- Rounding Decimals
