# Rounding Multi-Digit Numbers on a Number Line

Content Rounding Multi-Digit Numbers on a Number Line
Do you want to learn faster and more easily?

Then why not use our learning videos, and practice for school with learning games.

Rating

Be the first to give a rating!
The authors
Team Digital

## Basics on the topicRounding Multi-Digit 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 fast-moving 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.

### TranscriptRounding 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!"

## Rounding Multi-Digit Numbers on a Number Line exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Rounding Multi-Digit Numbers on a Number Line.
• ### Round to the nearest 100.

Hints

We 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.

Solution

42,329 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?

Hints

What 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?

Solution

27,348 rounded to the nearest 10 is 27,350.

• ### Round to the nearest 10.

Hints

When 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?

Solution

When 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.

Hints

If 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.

Solution

This is how the numbers should have been assigned.

• ### Round to the nearest 1,000.

Hints

When 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?

Solution

24,658 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.

Hints

Try 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?

Solution

The 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.