Multiplying and Dividing Decimals –

Multiplying and dividing decimals without a calculator is a key non-calculator skill tested on Foundation and Higher GCSE Maths papers. The technique relies on ignoring the decimal point, performing the calculation with whole numbers, and then repositioning the point.

What Is Decimal Multiplication and Division?

When you multiply or divide decimals, you apply the same techniques as with whole numbers but must manage the position of the decimal point carefully.

For multiplication, the total number of decimal places in the answer equals the total number of decimal places in the numbers being multiplied. For division, you can convert the divisor to a whole number by multiplying both the divisor and dividend by the same power of 10.

These methods work for any decimal calculation and are essential on non-calculator papers.

Key Formulas

Step-by-Step Method

Multiplying Decimals

1. Ignore the decimal points and multiply the numbers as whole numbers.
2. Count the total number of decimal places in both original numbers.
3. Place the decimal point in your answer so it has that many decimal places.

Dividing Decimals

1. If the divisor is a decimal, multiply both the dividend and divisor by 10 (or 100, 1000) until the divisor is a whole number.
2. Perform the division as normal.
3. The decimal point in the answer sits directly above its position in the dividend.

Worked Example 1 — Foundation Level

Question: Calculate 0.3 × 0.7.

Working:

Step 1 — Ignore decimals: 3 × 7 = 21.

Step 2 — Count decimal places: 0.3 has 1 dp, 0.7 has 1 dp. Total = 2 dp.

Step 3 — Place the point: 21 becomes 0.21.

Answer: 0.21

Worked Example 2 — Higher Level

Question: Calculate 3.42 × 2.5 without a calculator.

Working:

Step 1 — Ignore decimals: 342 × 25. Break this down: 342 × 25 = 342 × 100 ÷ 4 = 34,200 ÷ 4 = 8,550. Alternatively: 342 × 20 = 6,840 and 342 × 5 = 1,710. Sum: 6,840 + 1,710 = 8,550.

Step 2 — Count decimal places: 3.42 has 2 dp, 2.5 has 1 dp. Total = 3 dp.

Step 3 — 8550 with 3 dp = 8.550 = 8.55.

Answer: 8.55

Worked Example 3 — Exam Style

Question: Calculate 14.4 ÷ 0.06.

Working:

Step 1 — Make the divisor a whole number. Multiply both by 100: 14.4 × 100 = 1,440 and 0.06 × 100 = 6.

Step 2 — Divide: 1,440 ÷ 6 = 240.

Answer: 240

Common Mistakes

• Placing the decimal point incorrectly after multiplying. Always count the total decimal places from the original numbers, not from the product of the whole numbers.
• Forgetting to adjust both numbers when dividing. When you multiply the divisor by 10, you must also multiply the dividend by 10 to keep the calculation equivalent.
• Dropping trailing zeros. When counting decimal places, include any trailing zeros — 2.50 counts as 2 decimal places.

Exam Tips

• For multiplying, use partitioning or the grid method if long multiplication feels tricky.
• Always do a rough estimate first (e.g. 3.42 × 2.5 ≈ 3 × 3 = 9) to check your answer is reasonable.
• On division questions, convert to a whole-number divisor immediately — it makes the working far simpler.

Practice Questions

Q1 (Foundation): Calculate 0.4 × 0.8.

Q2 (Foundation): Calculate 6.3 ÷ 0.9.

Q3 (Higher): Calculate 0.045 × 200.

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Related Topics

• Decimals
• Order of Operations (BIDMAS)
• Rounding: Decimal Places and Significant Figures

Summary

• To multiply decimals, multiply as whole numbers then place the decimal point using the total count of decimal places.
• To divide by a decimal, multiply both numbers by 10 (or 100) to make the divisor a whole number, then divide.
• Always estimate first to check your answer is in the right ballpark.
• Count decimal places carefully — this is where most errors occur.