Rounding MultiDigit Numbers on a Number Line
Basics on the topic Rounding MultiDigit Numbers on a Number Line
In this Rounding using a Number Line video…
Sklyar and Henry are at the train station waiting for the train to take them to see their favourite band, KIDS. Henry and Sklyar notice the fastmoving numbers of the passenger counter and can’t keep their eyes off it! They want to try to work out approximately how many passengers come through the train station so they use rounding on a number line to come up with some estimates!
Rounding on 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.
Rounding to the nearest thousand number line, rounding to the nearest 100 number line and rounding to the nearest 10 number line are all possible. In this video, you will see Skylar and Henry try all three.
Steps for number line rounding
To round label the ends of the number line with the benchmark numbers based on the rounded place value. For example, if we were rounding to the nearest thousand, we would look at the number in the thousands place, in this case 2. We can then label each end of the number line as 32,000 and 33,000 as these are the thousand below and above our number.
Count the increments on the line and label the midpoint. As we can see above, in this case it is 32,500.
Find about where we would put the number on the line then: * If the number is closer to the lower benchmark number, round down to the smaller number. * If the number is closer to the larger benchmark number, round up to the bigger number.
Here, the number is past the midpoint so is closer to the larger benchmark number meaning we round up.
Additional Number Line Rounding Practice
Following the video, there is continued rounding numbers on a number line practice with our rounding number line interactive exercises and our rounding using a number line worksheet.
Transcript Rounding MultiDigit 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 MultiDigit 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 thirtytwo thousand, six hundred and ninetyfour 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 thirtytwo thousand, and thirtythree 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 thirtytwo thousand, five hundred. Now, find out about where the number would be on the line. Thirty two thousand, six hundred and ninetyfour 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, thirtythree thousand passengers. We could take the SAME number and round it to a DIFFERENT place value. Let’s look at rounding thirtytwo 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? Thirtytwo thousand, SIX hundred. And which number is on this end? Thirtytwo 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 thirtytwo thousand, seven hundred. We round UP and say APPROXIMATELY thirtytwo 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 thirtytwo thousand, six hundred and ninety on this end and thirtytwo thousand, seven hundred on this end. What do we count the increments by? Ones. Put the midpoint here, thirtytwo thousand, six hundred and ninetyfive. The number we are rounding goes HERE. Do we round the number UP or DOWN? We would round down and say there are approximately thirtytwo 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!"
Rounding MultiDigit Numbers on a Number Line exercise

Round to the nearest 100.
HintsWe need to find the hundred above and below 42,329. Imagine counting up in hundreds, 42,100, 42,200, ...
What number is halfway between the two hundreds? It will need to end in 50.
Look at the digit to the right of the hundreds. If it below 5 we round down, if it is 5 or higher, we round up.
Solution42,329 rounded to the nearest 100 = 42,300.
The hundred below is 42,300 and the hundred above is 42,400.
The digit to the right of the hundred in 42,329 is 2, so we round down.

What is the number rounded to the nearest 10?
HintsWhat is the digit to the right of the tens place? Is it 5 or higher?
The tens either side would be 27,340 and 27,350. Which of these numbers is the passenger number closer to?
Solution27,348 rounded to the nearest 10 is 27,350.

Round to the nearest 10.
HintsWhen rounding to the nearest 10, look at the digit to the right of the tens column. If this is below 5, round down.
If the number to the right of the tens column is 5 or higher, round up.
Try drawing a number line with the nearest ten either end. Which ten is your number nearest to?
SolutionWhen rounding to the nearest 10, look at the digit to the right of the tens column. If it is 5 or higher, round up; if it lower than 5, round down.
Rounded to the nearest 10:
 23,468 = 23,470
 25,153 = 25,150
 34,681 = 34,680
 40,057 = 40,060

Round to the nearest 10, 100 and 1,000.
HintsIf you are rounding to the nearest 1,000, look at the digit to the right of the thousands column. If it is 5 or higher round up, if it below 5, round down.
If you are rounding to the nearest 100, look at the digit to the right of the hundreds column. If it is 5 or higher, round up.
If you are rounding to the nearest 10, look at the digit to the right of the tens column. If it is 5 or higher, round up.
SolutionThis is how the numbers should have been assigned.

Round to the nearest 1,000.
HintsWhen rounding to the nearest 1,000, look at the digit to the right of the thousands column. In 24,658, what is the digit to the right of the thousands column?
If the number to the right of the thousands column is 5 or higher, round up. What is the digit to the right of the thousands column?
Look at the half way point on the number line. Is the number Henry and Skylar are rounding higher or lower than the midpoint?
Solution24,658 rounded the nearest 1,000 is 25,000.
The two markers either end are the thousand below, 24,000 and the thousand above, 25,000.
The halfway marker is 24,500.
The number to the right of the thousands place is 6, so we round up.

Rounding at the concert.
HintsTry drawing a number line and marking on the numbers 10 below and above 46,130.
Using your number line, which numbers would round up to 46,130?
Using your number line, which numbers would round down to 46,130?
SolutionThe number line shows how, when 46,130 is the number we are rounding to, to the nearest 10, the numbers that would round up to this are: 46,125; 46,126; 46,127; 46,128 and 46,129.
The numbers that would round down to this are: 46,131; 46,132; 46,133 and 46,134.
The number could also be 46,130.
Rounding (Tens)
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Rounding MultiDigit Numbers
Rounding MultiDigit Numbers on a Number Line
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