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Level 7Grade 7skill: decimal_multiply· 9 min read

How to Multiply Decimals

In short: Multiply decimals by ignoring the points, multiplying as whole numbers, then giving the answer as many decimal places as both factors had combined. So 0.3 × 0.2 = 0.06, not 0.6 — count the places every time, and estimate to check the size.

Multiply the digits first, place the point last

Here is the whole method in one sentence: ignore the decimal points, multiply as if they were whole numbers, then give the answer as many decimal places as the two factors had put together. That last clause is where almost every mark is won or lost.

Take 0.3 × 0.2. Strip the points and you are just doing 3 × 2 = 6. Now count decimal places: 0.3 has one, 0.2 has one, so the answer needs two. Two places from the right of 6 lands you at 0.06 — you have to write a zero in front to get there. The tempting answer 0.6 is exactly one place out, and it is wrong. Multiplying two numbers each smaller than 1 must give something smaller than either of them, and 0.06 < 0.2 while 0.6 > 0.2. The size test catches the slip on its own.

The reason the digit-count works is simple: 0.3 is 3 ÷ 10 and 0.2 is 2 ÷ 10, so their product carries a ÷ 100 — two tens, two decimal places. You are just keeping score of the tens.

  1. Ignore both decimal points and multiply the numbers as whole numbers.
  2. Count the total number of decimal places in the two factors combined.
  3. Put the point in the product that many places from the right, adding leading zeros if you run out of digits.
  4. Estimate to check: a quick rounding of the factors should land near your answer.

The decimal-to-fraction shortcuts worth memorising Why it works

0.5 = 1/2
Multiplying by 0.5 halves the other number.

0.5 × 4.8 = 2.4 (half of 4.8).

0.25 = 1/4
Multiplying by 0.25 divides the other number by 4.

0.25 × 3.6 = 3.6 ÷ 4 = 0.9.

0.2 = 1/5
Multiplying by 0.2 divides the other number by 5.

0.2 × 35 = 35 ÷ 5 = 7.

0.1 = 1/10
Multiplying by 0.1 shifts the point one place left.

0.1 × 7.5 = 0.75.

Under exam pressure the fastest route is often not the algorithm at all — it is recognising that a decimal is a friendly fraction in disguise. When you see 0.25 × 3.6, dividing 3.6 by 4 beats setting out a long multiplication, and it sidesteps the place-counting trap entirely.

Worked examples

Compute 0.3 × 0.2. = 0.06
  1. Ignore the points: 3 × 2 = 6.
  2. Count decimal places: 0.3 has 1, 0.2 has 1, total 2.
  3. Write 6 with two decimal places: 0.06 (a leading zero is needed).
Compute 1.2 × 0.05. = 0.06
  1. Ignore the points: 12 × 5 = 60.
  2. Count decimal places: 1.2 has 1, 0.05 has 2, total 3.
  3. Write 60 with three decimal places: 0.060 — the trailing zero drops, leaving 0.06 (same value, but reached a different way from the example above).
A £240 coat is reduced by 15% in a sale. What do you pay? = £204
  1. Write 15% as a decimal: 15% = 0.15.
  2. Find the discount: 0.15 × 240 = 36, so the coat is £36 off.
  3. The question asks the price paid, not the discount: 240 − 36 = 204.
Find 0.25 × 3.6 using a shortcut. = 0.9
  1. Recognise that 0.25 = 1/4.
  2. Multiplying by a quarter is dividing by 4: 3.6 ÷ 4 = 0.9.
  3. Check with the digit rule: 25 × 36 = 900, three decimal places gives 0.900 = 0.9.
Fuel costs £1.45 per litre and you buy 6.5 litres. What is the cost? = £9.43 (9.425 exactly)
  1. Ignore the points: 145 × 65 = 9425.
  2. Count decimal places: 1.45 has 2, 6.5 has 1, total 3.
  3. Place the point: 9.425, which rounds to £9.43.

Six ways this goes wrong

Losing a decimal place

✗ 0.3 × 0.2 = 0.6

The digits (3 × 2 = 6) are right, but the point is one place too far to the right.

Fix: Count every decimal place in both factors before you write the answer: 1 + 1 = 2 places, so 6 becomes 0.06, not 0.6.

decimal_point_shift

Adding instead of multiplying

✗ 0.3 × 0.2 = 0.5

A student reads the numbers and defaults to addition, getting 0.3 + 0.2 = 0.5. The operation, not the arithmetic, is wrong.

Fix: Multiplication of the digits gives 3 × 2 = 6, then two decimal places gives 0.06. If the word problem says 'of', 'per', or 'times', it is multiplication.

wrong_operation

Stopping at the discount

✗ The £240 coat with 15% off costs 36

0.15 × 240 = 36 is correct — but 36 is the discount, an intermediate value, not the price paid. The student stopped one step early.

Fix: Subtract the discount from the original: 240 − 36 = £204. Re-read the question to see which quantity it actually asks for.

partial_computation

Using the percent number raw

✗ 15% of £240 = 15

The percent sign was ignored and the number 15 was treated as the answer. A percentage is a fraction of the base, not the base's replacement.

Fix: Convert first: 15% = 0.15, then 0.15 × 240 = 36. The '%' means 'divide by 100', so 15% is 0.15.

percent_as_whole

Taking the percentage of the wrong base

✗ A lamp costs £50 and is marked up 20% to sell at £60, so profit = 12

The 20% markup is 20% of the £50 cost, not the £60 selling price. Using 0.20 × 60 = 12 measures against the wrong base.

Fix: Anchor the percentage to the stated base: 0.20 × 50 = £10 profit, which checks out as 50 + 10 = £60.

base_confusion

Mixing hours with minutes

✗ At 0.8 km per minute for 1.5 hours you travel 1.2 km

0.8 × 1.5 = 1.2 multiplies a per-minute rate by a time in hours. The units do not match, so the product is meaningless.

Fix: Convert to one unit first: 1.5 hours = 90 minutes, then 0.8 × 90 = 72 km.

unit_mismatch

Practice: multiplying decimals

Work through these decimal multiplication problems. Count decimal places carefully, and watch for the percentage and word-problem traps.

Related skills

First, make sure of

Frequently asked questions

Why is 0.3 × 0.2 equal to 0.06 and not 0.6?

Multiply the digits first: 3 × 2 = 6. Then count the decimal places in the factors — 0.3 has one and 0.2 has one, so the answer needs two decimal places. Two places from the right of 6 gives 0.06. A quick sanity check confirms it: multiplying two numbers each below 1 must give something smaller than both, and 0.6 is larger than 0.2, so 0.6 cannot be right.

How do I count decimal places when the factors have different amounts?

Add them together. For 1.2 × 0.05, the factor 1.2 has one decimal place and 0.05 has two, so the product needs three. Since 12 × 5 = 60, you write 60 with three decimal places as 0.060, and the trailing zero drops to leave 0.06. Always total the places across both numbers — do not just use the larger one.

How do I turn a percentage into a decimal multiplication?

Divide the percent by 100 to get a decimal, then multiply. 15% becomes 0.15, so 15% of 240 is 0.15 × 240 = 36. Watch two traps: do not use the number 15 directly as the answer, and re-read whether the question wants the part (the 36) or the whole after a change, such as 240 − 36 = 204 for a sale price.

Is there a faster way than long multiplication for decimals like 0.25?

Yes — recognise the decimal as a fraction. 0.25 = 1/4, so 0.25 × 3.6 is just 3.6 ÷ 4 = 0.9. Likewise 0.5 halves, 0.2 divides by 5, and 0.1 shifts the point one place left. These shortcuts are quicker and avoid place-counting errors entirely.

What is the single most common mistake to avoid?

Misplacing the decimal point by one position, usually by forgetting a leading zero. The fix is a habit: count the total decimal places before writing the answer, insert leading zeros if the digits run out, and then estimate. If your answer is ten times too big or too small, a place-value slip is almost always the cause.