Decimals and Percentages · Grade 6

How do you multiply two decimals and where does the point go?

Multiply the digits as though there were no decimal point at all, then count how many digits follow the point in the two factors together. That total is how many digits follow the point in the answer. When dividing by a whole number, carry the division past the point and add zeros as needed.

Learning objectives

Multiply first, count second

Ignore the points and multiply the numbers as whole numbers. This is a multiplication you already know how to do, with no new rule attached.

Then count the digits after the point in both factors and add. If one has two and the other one, the answer has three.

The reason is simple: each digit after the point is a division by ten. Two divisions by ten plus one more is a division by a thousand, which is three digits.

You can see it on a small example. Three tenths times four tenths is twelve hundredths, because a tenth times a tenth is a hundredth — which is exactly what counting two digits says. The rule is not a trick but shorthand for that sentence.

Why multiplying can make things smaller

Multiplying by a number less than one gives an answer smaller than what you started with. Half of eight is four, and nobody finds that surprising — but the same statement written as 0.5 times 8 often does surprise.

So the rule that multiplication always makes things bigger is not true, and this is exactly where it breaks. It is worth saying out loud, because it contradicts an intuition built up over every earlier school year.

Division that carries on past the point

When a division by a whole number does not come out exactly, do not stop with a remainder. Put a point in the answer, add a zero to what is left, and carry on — trailing zeros change nothing.

Continue until the division ends or until you have the number of digits the question asked for. A good final check is to multiply your answer by the divisor and see that you get back to where you started.

Worked examples

  1. Calculate 0.3 times 0.4

    1. Multiply without points: 3 times 4 is 12
    2. Count digits after the point: one and one, so two in total
    3. The answer therefore has two digits after the point

    Answer: 0.12 — smaller than both factors, since both are less than one

  2. Calculate 2.5 times 1.2

    1. Multiply without points: 25 times 12 is 300
    2. Count: one digit and one digit, so two in total
    3. Place the point: 3.00

    Answer: 3

  3. Calculate 7 divided by 4

    1. 4 goes into 7 once, leaving a remainder of 3
    2. Put a point in the answer and a zero on the remainder: 30
    3. 4 goes into 30 seven times, leaving 2
    4. Add another zero: 4 goes into 20 exactly five times

    Answer: 1.75

Common mistakes

Lining up by the point in multiplication too
Lining up by the point belongs to addition and subtraction only. In multiplication you multiply as whole numbers and count digits at the end, and no lining up is needed.
Counting the digits of only one factor
The number of digits in the answer is the sum from both factors. Counting only one puts the point one place too far right, and the answer is ten times too large.
Assuming multiplication always increases
Multiplying by less than one decreases. It is the same fact as half of eight, written as a decimal, and it is useful as a check on the answer.

What to remember

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