Dividing by 10, 100 and 1,000

Dividing by ten moves every digit one place to the right. Digits that move past the ones place become tenths, hundredths and thousandths, so a decimal point is often needed where there was none before.

The pattern

Notice the last line. Once digits pass the ones place a decimal point is required, and a zero goes in front of it so the point cannot be missed. .42 and 0.42 are the same number, and the second is much harder to misread.

Why crossing off a zero is a trap

Crossing off a trailing zero happens to work for 4,200 / 10. It gives no answer at all for 4,237 / 10, which has no zero to cross off. Moving the digits handles both: 423.7.

Dividing by multiples of ten

To divide by a number like 40, divide by 10 first and then by 4. Splitting the divisor into a power of ten and a single digit keeps both steps easy.

The order does not matter. Dividing by four first gives 900, and then by ten gives 90 again.

Checking the answer

Multiplication undoes division, so a quick check costs a few seconds. If 6,504 / 100 = 65.04, then 65.04 x 100 should return 6,504, and the digits should move two places back to the left.

Common mistakes

Forgetting the leading zero

Write 0.42, not .42. A point at the start of a line is easy to lose, and losing it multiplies the answer by a hundred.

Moving the wrong way

Dividing makes a number smaller, so the digits move right. If your answer came out bigger than what you started with, the digits went the wrong way.

Check yourself