Calculate 3.7 times 10

Every digit moves up one place. The 7, which was a tenth, becomes a one. The 3, which was a one, becomes a ten. 37

Calculate 0.4 times 100

A hundred has two zeros, so two places up. The 4, which was a tenth, becomes a ten. This gives 40. 40

How many centimetres are in 2.35 metres?

There are 100 centimetres in a metre, so multiply by 100. Move two places up. 2.35 becomes 235. 235 centimetres

Decimals and Percentages · Grade 6

What happens when you multiply a decimal by ten or a hundred?

Every digit moves up one place for each multiplication by ten, and down one place for each division. In writing it looks as though the point moves, but what actually moves is the digits: multiplying by ten turns tenths into ones. This is why you do not add a zero to a decimal when multiplying by ten.

Learning objectives

Multiply and divide a decimal by ten, a hundred and a thousand
Explain the movement in terms of place value rather than as a trick with the point
Convert between metres and centimetres, and between kilograms and grams, by the same movement

What actually moves

Multiplying by ten makes every digit ten times larger, which is to say it moves up one place: hundredths become tenths, tenths become ones, ones become tens.

In writing it is convenient to say the point moves right, and that works. But someone who remembers only the mechanical rule forgets it under pressure, while someone who understands that the digits move up can always reconstruct it.

Each zero in the multiplier is one place. Multiplying by a hundred moves two places, by a thousand three, and dividing does exactly the reverse.

Why you do not add a zero

With whole numbers, multiplying by ten looks like adding a zero, and that is misleading. What happened is that every digit moved up a place and the zero merely filled the ones place that was vacated.

In a decimal there is no vacated place at the end, because digits are already there. 3.7 times ten is 37, not 3.70.

Unit conversion is the same thing

There are a hundred centimetres in a metre, so converting metres to centimetres is multiplying by a hundred — two places up. The other direction is dividing by a hundred.

There are a thousand grams in a kilogram, so there the shift is three places. Anyone who understands the shift does not need to memorise a conversion table, only the number of zeros.

Note that this only works for units whose ratio is ten, a hundred or a thousand. An hour has sixty minutes, not a hundred, so converting hours to minutes is not a shift of places but a multiplication by sixty — which is exactly why it pays to check the ratio before moving anything.

Worked examples

Calculate 3.7 times 10
1. Every digit moves up one place
2. The 7, which was a tenth, becomes a one
3. The 3, which was a one, becomes a ten
Answer: 37
Calculate 0.4 times 100
1. A hundred has two zeros, so two places up
2. The 4, which was a tenth, becomes a ten
3. This gives 40
Answer: 40
How many centimetres are in 2.35 metres?
1. There are 100 centimetres in a metre, so multiply by 100
2. Move two places up
3. 2.35 becomes 235
Answer: 235 centimetres

Common mistakes

Adding a zero when multiplying by ten: That works only for whole numbers, and for a different reason. With a decimal the answer is wrong: 3.7 times ten is 37, not 3.70, which is the same number you started with.
Shifting the wrong way when dividing: Division makes things smaller, so the digits move down a place. A result larger than the original after dividing means the shift went the wrong way.
Miscounting the zeros: A hundred has two zeros and a thousand three. Counting wrong shifts one place too far, and the answer is out by a factor of ten — usually obvious on a check.

What to remember

Multiplying by ten moves every digit up one place.
Each zero in the multiplier is one place.
Do not add a zero to a decimal.
Unit conversion is the very same shift.