Rounding Multi-Digit Numbers on a Number Line

"Skylar, I can’t stop staring at the numbers turning on that sign, it’s fascinating!" "I wonder how many passengers come through the train station each month?" "It won’t always be the same, so we can round that number to an approximate answer that will tell us ABOUT how many." Let's help Skylar and Henry determine an approximate number of train passengers using "Rounding Multi-Digit Numbers on a Number Line". Rounding numbers means adjusting the digits up or down to the nearest, tens, hundreds and thousands to make calculations easier. Number lines can help with rounding because we can visualise if our number should be rounded up or rounded down. In this month there are thirty-two thousand, six hundred and ninety-four passengers coming through the station. Let's round it to several different place values using a number line to find approximations, or estimates. First, we’ll round to the thousands place. To set up the number line, we will label the ends. To do this we need to think about the nearest thousand below our number and the nearest thousand above our number. This end is thirty-two thousand, and thirty-three thousand is on THIS end. Since we are rounding to the thousands place, our increment lines go up in steps of one hundred, so on the line we are counting by hundreds, and the midpoint is HERE at thirty-two thousand, five hundred. Now, find out about where the number would be on the line. Thirty two thousand, six hundred and ninety-four would be about HERE. The number we are rounding is past the midpoint and closer to the larger number. So when rounding to the thousands place, we would round UP and say, approximately, or ABOUT, thirty-three thousand passengers. We could take the SAME number and round it to a DIFFERENT place value. Let’s look at rounding thirty-two thousand, six hundred and ninety four to the HUNDREDS place. We label the ends this time thinking about which HUNDRED is the nearest below and above our number. Which number is on this end? Thirty-two thousand, SIX hundred. And which number is on this end? Thirty-two thousand, SEVEN hundred. What do we count the increments by? We count them by tens. What is the midpoint? The midpoint is thirty two thousand six hundred and fifty, and it goes HERE. Where do we put the number on the line? It goes about HERE. The number we are rounding is past the midpoint and closer to thirty-two thousand, seven hundred. We round UP and say APPROXIMATELY thirty-two thousand, seven hundred passengers.

To get the closest approximation, or estimate, we can even round this number to the TENS place! Which numbers should we label each end with? We have thirty-two thousand, six hundred and ninety on this end and thirty-two thousand, seven hundred on this end. What do we count the increments by? Ones. Put the midpoint here, thirty-two thousand, six hundred and ninety-five. The number we are rounding goes HERE. Do we round the number UP or DOWN? We would round down and say there are approximately thirty-two thousand, six hundred and ninety passengers. While Skylar and Henry wait for the next passenger to arrive, let's review. Remember, rounding numbers means adjusting the digits up or down to make calculations easier. The result will be an approximate answer rather than an exact one. Number lines can help with rounding because we can visualise if our number should be rounded up or rounded down. To round, label the ends of the number line with numbers based on the rounded place value. Count the increments on the line and label the midpoint. Find about where we would put the number on the line. If the number is closer to the lower number, round down to the smaller number. If the number is closer to the larger number, round up to the bigger number.

"Henry, do you notice that the number hasn't changed in a while?" "We MISSED our train and THE CONCERT!" "That's okay. ROUNDING ROCKS!" "ROUNDING ROCKS!"