Dividing by 10, 100 and 1000

Dividing by 10, 100 and 1000

Dividing by 10, 100 or 1000 is the reverse of multiplying by them. If multiplying makes a number ten times bigger by shifting digits left, then dividing makes it ten times smaller by shifting digits right.

If you have already met Multiplying by 10, 100 and 1000, this lesson will feel familiar — just run the same idea backwards.

The big idea: digits shift right

Our number system is built on groups of ten, as you saw in Place Value to Thousands. Each place is ten times the place to its right.

So when you divide by 10, every digit becomes ten times smaller and moves one place to the right into the next-smaller place.

Take 70. The 7 is in the tens place. Divide by 10 and the 7 shifts into the ones place — it is now worth 7. The 0 that was in the ones place is no longer needed.

70 ÷ 10 = 7

Dividing by 100 and 1000

The same idea repeats, one shift for each ten:

• ÷ 10 = 1 shift right (10 is one ten)
• ÷ 100 = 2 shifts right (100 = 10 × 10)
• ÷ 1000 = 3 shifts right (1000 = 10 × 10 × 10)

So the number of zeros in 10, 100 or 1000 tells you how many places to shift right.

Start	÷ 10	÷ 100	÷ 1000
3,000	300	30	3
8,000	800	80	8
12,000	1,200	120	12
25,000	2,500	250	25

Worked example 1: dividing by 10

Work out 360 ÷ 10.

1. 10 has one zero, so each digit shifts one place right.
2. The 3 moves from hundreds to tens (worth 30).
3. The 6 moves from tens to ones (worth 6).
4. The trailing 0 has nowhere lower to go, so it drops off.
5. Result: 30 + 6 = 36.

So 360 ÷ 10 = 36.

Worked example 2: dividing by 100

Work out 700 ÷ 100.

1. 100 has two zeros, so digits shift two places right.
2. The 7 starts in the hundreds place. Two shifts right lands it in the ones place → worth 7.
3. Both trailing zeros drop off.
4. Result: 7.

So 700 ÷ 100 = 7.

Worked example 3: dividing by 1000

Work out 5,000 ÷ 1000.

1. 1000 has three zeros, so digits shift three places right.
2. The 5 starts in the thousands place. Three shifts right lands it in the ones place → worth 5.
3. The three trailing zeros drop off.
4. Result: 5.

So 5,000 ÷ 1000 = 5. This makes sense: 5,000 is five groups of 1000, so dividing by 1000 leaves 5.

The shortcut and its trap

For whole numbers that end in enough zeros, here is the quick rule:

• ÷ 10 → remove one zero
• ÷ 100 → remove two zeros
• ÷ 1000 → remove three zeros

This works whenever there are enough trailing zeros to remove. But the trap is the same as with multiplying: it does not work when the answer is a decimal. For example, 35 ÷ 10 = 3.5, not 35 with a zero crossed out. That is why the safe rule to remember is digits shift one place right for each ten — it never lets you down.

Try it yourself

Solve these, then look for the pattern.

• 90 ÷ 10 = ? (Answer: 9)
• 900 ÷ 100 = ? (Answer: 9)
• 9,000 ÷ 1000 = ? (Answer: 9)
• 4,500 ÷ 100 = ? (Answer: 45)

Then pick a big number like 6,000 and divide it by 10, then 100, then 1000. Say out loud how many places the digits shift each time and watch the number shrink.

Great job!

You can now divide by 10, 100 and 1000 quickly, and you know the place-value reason behind it. Multiplying and dividing by these numbers are two sides of the same coin.

Look back at Multiplying by 10, 100 and 1000 to compare the two moves, or practise sharing into equal groups in Division Made Simple.