Multiplying Decimals by 10, 100 and 1000
Multiplying a decimal by 10, 100, or 1000 follows a simple pattern: the decimal point moves to the right. This is one of the most useful shortcuts in mathematics, used in unit conversions, money calculations, and scientific notation.
When you multiply by 10, the decimal point shifts 1 place right. By 100, it shifts 2 places. By 1000, it shifts 3 places. The number of zeros in the multiplier equals the number of places the decimal point moves.
What is Multiplying Decimals by 10, 100 and 1000 - Class 5 Maths (Decimals)?
Rule for multiplying decimals by powers of 10:
| Multiplied by | Decimal point moves | Direction |
|---|---|---|
| × 10 | 1 place | Right → |
| × 100 | 2 places | Right → |
| × 1000 | 3 places | Right → |
If the decimal point goes past the last digit, add zeroes as placeholders.
Multiplying Decimals by 10, 100 and 1000 Formula
Decimal × 10 = Shift decimal point 1 place right
Decimal × 100 = Shift decimal point 2 places right
Decimal × 1000 = Shift decimal point 3 places right
Solved Examples
Example 1: Example 1: Multiply by 10
Problem: Calculate 3.45 × 10.
Solution:
Move decimal 1 place right: 3.45 → 34.5
Answer: 3.45 × 10 = 34.5
Example 2: Example 2: Multiply by 100
Problem: Calculate 3.45 × 100.
Solution:
Move decimal 2 places right: 3.45 → 345
Answer: 3.45 × 100 = 345
Example 3: Example 3: Multiply by 1000
Problem: Calculate 3.45 × 1000.
Solution:
Move decimal 3 places right: 3.45 → 3450 (add a zero as placeholder)
Answer: 3.45 × 1000 = 3,450
Example 4: Example 4: Small decimal × 10
Problem: Calculate 0.078 × 10.
Solution:
Move decimal 1 place right: 0.078 → 0.78
Answer: 0.078 × 10 = 0.78
Example 5: Example 5: Small decimal × 1000
Problem: Calculate 0.006 × 1000.
Solution:
Move decimal 3 places right: 0.006 → 6
Answer: 0.006 × 1000 = 6
Example 6: Example 6: Word problem — Unit conversion
Problem: A ribbon is 2.75 metres long. Convert to centimetres (1 m = 100 cm).
Solution:
2.75 × 100 = 275
Answer: The ribbon is 275 cm long.
Example 7: Example 7: Word problem — Money
Problem: One chocolate costs ₹12.50. What is the cost of 10 chocolates?
Solution:
12.50 × 10 = 125.0 = 125
Answer: 10 chocolates cost ₹125.
Example 8: Example 8: Word problem — Weight
Problem: A packet weighs 0.453 kg. Convert to grams (1 kg = 1000 g).
Solution:
0.453 × 1000 = 453
Answer: The packet weighs 453 grams.
Example 9: Example 9: Pattern recognition
Problem: Complete the pattern: 0.025, ___, ___, ___ (multiply by 10 each time).
Solution:
0.025 × 10 = 0.25
0.25 × 10 = 2.5
2.5 × 10 = 25
Answer: 0.025, 0.25, 2.5, 25
Key Points to Remember
- Multiplying by 10 shifts the decimal point 1 place right.
- Multiplying by 100 shifts it 2 places right.
- Multiplying by 1000 shifts it 3 places right.
- The number of zeros in the multiplier = number of places the decimal shifts.
- If the decimal goes past all digits, add trailing zeroes (e.g., 2.5 × 100 = 250).
- This is useful for converting: m to cm (×100), km to m (×1000), kg to g (×1000).
- The digits themselves do not change — only the position of the decimal point changes.
Practice Problems
- Calculate 5.67 × 10.
- Calculate 0.045 × 100.
- Calculate 1.2 × 1000.
- Convert 3.5 km to metres.
- A notebook costs ₹18.75. Find the cost of 100 notebooks.
- Calculate 0.009 × 1000.
- Fill in the blank: 0.34 × ___ = 340.
- Convert 0.875 litres to millilitres (1 L = 1000 mL).
Frequently Asked Questions
Q1. Why does multiplying by 10 shift the decimal point?
Multiplying by 10 makes each digit 10 times larger. A digit in the tenths place moves to the ones place, ones moves to tens, and so on. This is equivalent to shifting the decimal point one place to the right.
Q2. What if I need to add zeroes when shifting?
If the decimal point moves past the last digit, add zeroes as placeholders. For example, 2.5 × 100: shift 2 places right gives 250 (a zero is added because there was only one digit after the decimal).
Q3. Does this rule work for any decimal?
Yes. The rule works for all decimals regardless of how many digits they have. The decimal point always shifts right by the number of zeroes in the multiplier.
Q4. How is this used in unit conversion?
Many unit conversions involve multiplying by 10, 100, or 1000. For example: metres to centimetres (×100), kilometres to metres (×1000), litres to millilitres (×1000), kilograms to grams (×1000).
Q5. What if I multiply by 10,000?
The decimal point shifts 4 places to the right, since 10,000 has 4 zeroes. For example, 0.0356 × 10,000 = 356.
Q6. Is multiplying by 10 the same as adding a zero?
For whole numbers, multiplying by 10 adds a zero at the end (5 × 10 = 50). For decimals, it shifts the decimal point. 5.3 × 10 = 53 (not 5.30). The 'add a zero' shortcut only works for whole numbers.
Q7. Can I use this to multiply by 20, 200, or 300?
Yes. Break it down: multiply by the non-zero part first, then shift for the zeroes. For example, 3.5 × 200 = 3.5 × 2 × 100 = 7 × 100 = 700.
Q8. What is the reverse operation?
The reverse is dividing by 10, 100, or 1000, which shifts the decimal point to the left by the same number of places.
Related Topics
- Multiplication of Decimals
- Dividing Decimals by 10, 100 and 1000
- Decimals (Grade 5)
- Comparing and Ordering Decimals
- Addition of Decimals
- Subtraction of Decimals
- Division of Decimals
- Converting Fractions to Decimals (Grade 5)
- Converting Decimals to Fractions
- Decimal Word Problems (Grade 5)
- Decimal Place Value (Grade 5)
- Rounding Decimals
