GCSE Maths Practice: decimals
This question helps you practise multiplying decimals by powers of ten — 10, 100, or 1000. It builds confidence in understanding how place values shift in GCSE Maths.
Each zero in the multiplier moves the digits one place to the right. Multiplying by 10 shifts one place, by 100 shifts two, and by 1000 shifts three.
Understanding Place Value Shifts
When multiplying by powers of ten (10, 100, 1000, etc.), each zero means the digits move one place to the right. The number becomes ten times larger with each shift. This method works for both whole numbers and decimals.
Decimals follow the same rule as whole numbers: multiplying by 10 moves every digit one place to the right of the decimal point. Dividing by 10 does the opposite — it moves digits one place to the left, making the number ten times smaller.
Step-by-Step Method
- Count how many zeros are in the multiplier.
- Move the decimal point that many places to the right (for multiplication).
- Fill any empty spaces with zeros as needed.
- Write your new number clearly without changing the digit order.
Worked Examples
Example 1: 0.4 × 10 = 4
Move one place right → 4.0 = 4.
Example 2: 0.4 × 100 = 40
Move two places right → 40.0 = 40.
Example 3: 0.45 × 1000 = 450
Move three places right → 450.0 = 450.
Example 4: 3.2 × 10 = 32
Move one place right → 32.0 = 32.
Notice how multiplying by powers of ten doesn’t change the digits themselves — it only changes their positions.
Common Mistakes
- Moving the decimal the wrong way: Multiplying always moves it right; dividing moves it left.
- Forgetting the number of zeros: Multiplying by 100 means two shifts, not one.
- Adding extra zeros unnecessarily: Only fill empty place values when needed, not more.
Real-Life Applications
Understanding place value shifts helps when converting between units (metres to centimetres, kilograms to grams) or calculating money. For example, £0.3 × 100 = £30 in pennies. In measurements, 0.45 m × 100 = 45 cm. Knowing how to move the decimal quickly saves time and avoids calculator mistakes in GCSE exams.
FAQs
1. Why does the decimal move right when multiplying?
Because each power of ten increases the number’s size by a factor of ten.
2. Does it matter if I move the digits or the decimal point?
No — they’re equivalent ways to think about the same shift.
3. What happens when there aren’t enough digits?
Add zeros to fill the empty places after the shift.
4. What about dividing by 10, 100, or 1000?
Move the decimal left by one, two, or three places instead.
Study Tip
Practise quick mental checks: 0.4 × 10 = 4, 0.4 × 100 = 40, 0.4 × 1000 = 400. The pattern builds intuition for scaling numbers up or down without a calculator.
Mastering how decimals move when multiplying by powers of ten strengthens number fluency across measurement, ratio, and unit conversion topics in GCSE Maths.