Rounding whole numbers

Round sixty three thousand, eight hundred and fifty two to the nearest hundred. Try it first. Pause if you like. We need the nearest hundred. Which digit is just to the right of the hundreds place? Look at the tens place. The digit there is 5. 5 and greater than 5 rounds up. Add 1 to the digit in the hundreds place. The rounded number is sixty three thousand, nine hundred. Put zeros in the tens and ones places. Write to the nearest hundred in brackets, so the rounding place is clear. The next digit decides. 5 and greater than 5 rounds up.

The number of people at a match, rounded to the nearest thousand, is thirty eight thousand. Part a. What is the smallest possible number of people at the match? Part b. What is the greatest possible number of people at the match? Try it first. Pause if you like. Now work backwards. Which whole numbers could round to thirty eight thousand? For the smallest number, we round up to thirty eight thousand. Rounding up adds 1 to the thousands digit, so before rounding the thousands digit is 7, because 7 plus 1 is 8. Now look at the hundreds place. To round up, it must be 5 and greater than 5. The smallest digit we can use is 5. The tens and ones are both 0. So the smallest possible number is thirty seven thousand, five hundred. For the greatest number, we round down to thirty eight thousand. Rounding down keeps the thousands digit, 8. Now look at the hundreds place. To round down, it must be 4 and smaller than 4. The greatest digit we can use is 4. Make the tens and ones as large as possible: both are 9. The next halfway tick is where rounding up begins. The greatest whole number must be just before it. So the greatest possible number is thirty eight thousand, four hundred and ninety nine. The next whole number has 5 hundreds, so it would round up. Our greatest number is just before that tick. The next digit decides. 5 and greater than 5 rounds up, and 4 and smaller than 4 rounds down.