When rounding to the nearest thousand, which digit do you look at?

On the left is the number. The card top right picks out the hundreds digit that decides the rounding; the card bottom right shows the number rounded to the nearest thousand. Change the number and both cards move. Picking out a single digit takes a slightly long formula in the top right card — just read the bold number underneath it.

Not the thousands digit

"To the nearest thousand" makes you want to look at the thousands digit. But the digit that decides is the one just below it: the hundreds.

The thousands digit is the one you keep. Everything from the hundreds down is what you turn into zeros. The top digit of that part, the hundreds, decides whether the thousands digit goes up or stays.

Take 34,567

Laid out digit by digit:

• Ten thousands — 3
• Thousands — 4
• Hundreds — 5
• Tens — 6
• Ones — 7

You are keeping the thousands, so look at the next digit down, the hundreds: 5. That is 5 or more, so the thousands digit goes from 4 to 5, and everything below it becomes 0: 35,000.

Take 34,499

The hundreds digit is 4. That is less than 5, so the thousands digit stays at 4, and everything below it becomes 0: 34,000.

34,499 and 34,500 are only 1 apart, but they round to 34,000 and 35,000, because the hundreds digit changes from 4 to 5.

5 is the dividing line

Set the number on the board to each of these.

Whether the thousands digit is 4 or 5, the hundreds digit is what decides. A hundreds digit of 4 or less leaves the thousands digit as it is; 5 or more moves it up by one.

Try it yourself

You can type the number on the board, or change it 1 at a time with − and +. Set it to 34,499 and press +: at 34,500 the result switches to 35,000.

• 34,498 — hundreds digit 4 → 34,000
• 34,499 — hundreds digit 4 → 34,000
• 34,500 — hundreds digit 5 → 35,000
• 34,501 — hundreds digit 5 → 35,000

The boundary is 34,500. Everything from 34,500 to 35,499 rounds to 35,000; one step below, 34,499 rounds to 34,000.

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