**Dividing by 10 or 100**

Now we’ve had a good look at place value here and here, we can go on to explore what happens when you divide or multiply by 10 or 100. Place value is all about 10s.

Take the number 57. If we multiply by 10, it becomes 570. Now we know that moving from Units to Tens to Hundreds means we multiply by 10 each time. So what we’ve done is taken the ‘5’ from the tens column and moved it to the hundreds column. Likewise, we’ve taken the ‘7’ from the from the units and moved it over to the tens. Finally we put a zero on the end to show it’s now a three digit number. See also **Zero as P****laceholder **below.

This process, like so many in maths, is reversible. The inverse of multiply is divide. So if we’re dividing by 10, then we’re moving the other way.

So 380 divided by 10 would become 38.

This approach is also useful when we’re dealing with decimals. So in another case:

75 divided by 10 is 7.5

Notice how the 5 has skipped over the decimal point? When we divide by 100 we’re moving two decimal places (two columns).

So 380 divided by 100 is 3.8. I put the dotted zero in to remind you what the number looked like before it was divided.

Don’t forget you can add a decimal point and zeroes to a whole number to help you remember all the places if you need to. We do this all the time with money. So if we have £1 coin and a 50p coin, we would say we had £1.50 not £1.5. That extra zero is a **placeholder** and it just reminds us there are no hundredths (or pennies) in this number.

**Zero as a placeholder**

The zero is used as a placeholder. It’s there to hold the space when there’s no other number to take its place. So in the number ‘307’ there’s no tens, but if we didn’t have the zero there we’d just have 37 and it would be a completely different number altogether. If you like, the zero is acting as a ‘referee’ in keeping the 3 and the 7 apart and in their correct places.

**TRY IT OUT **

You can see this yourself by using a calculator and multiplying or dividing by 10 or 100. Try lots of different numbers with a decimal point in and see what happens to the number. Look for the change in where the decimal point is. Let me know what you find.

Katherine says

Great article, Liz! Love the suggestion to try it on my calculator – that’s an excellent way to see what’s happening.