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Rounding Multi-Digit Numbers

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Basics on the topic Rounding Multi-Digit Numbers

Rounding in Maths

What is rounding? Rounding numbers is a way of simplifying a number. When we round, our number will be an approximate answer, not an exact one. We can round to any place value of a multi-digit number by using the rules for rounding. For example, we can do rounding to the nearest 10, 100 and 1000.

Rules for Rounding

What strategies can you use when rounding multi-digit numbers? These are the rules for rounding multi-digit numbers up and down.

# Rule
1 Identify the place value being rounded
and underline the digit.
2 Next, find the place value of the digit
to the right and circle it.
3 If the number is 0 to 4, the
number stays the same. If the number
is 5 to 9, it gets rounded up.

Rounding – Example

Let’s have a look at an example. We use the number 47,326. To make the operation of rounding easier to follow, we put our example number into a place value chart.

TT T H T O
4 7 3 2 6

Now, remembering the rules of rounding and the necessary steps, we can begin rounding the number up. We begin looking at the ten-thousands place.

  • First, identify the place value being rounded and UNDERLINE the digit. In the example below, we are rounding to the nearest ten thousand so we underline the digit in the ten thousands place.
  • Next, find the place value of the digit to the RIGHT and CIRCLE it. In this example, the digit to the right is the thousands digit so we circle the number in the thousands place. This number will tell us what we need to do.

SEO_25206_line_10.svg

If the number you are rounding is followed by zero to four, the number being rounded STAYS THE SAME.

SEO_25206_line_14.svg

If the number you are rounding is followed by five to nine, round the number UP to the NEXT NUMBER because it is closer to the next whole number. In this case, the number in the thousands place is 7. Since we are rounding to the nearest 10 000, this means that we are rounding up as seven is between five and nine.

SEO_25206_line_16.svg

Finally, all the remaining place values AFTER the rounded number are replaced with zeros.

SEO_25206_line_17.svg

Rounding Numbers – Summary of Steps

Remember, these are the steps for rounding multi-digit numbers to the nearest 10, 100 or 1,000:

# Rule
1 Identify the place value being rounded
and underline the digit.
2 Next, find the place value of the digit
to the right and circle it.
3 If the number is 0 to 4, the
number stays the same. If the number
is 5 to 9, it gets rounded up.

Do you want some more practice? After watching the video, you can practise rounding multi-digit numbers to any place value with our interactive exercises and rounding multi-digit numbers worksheets for KS2. The rounding video, exercises, and multi-digit worksheet will help you understand how to round numbers with many digits and to any place value.

Transcript Rounding Multi-Digit Numbers

Skylar wants to know approximately how far away different objects are from the ground. We can help her find approximate distances by "Rounding Multi-Digit Numbers" to any place value.
Rounding numbers is a way of simplifying a number. When we round, our number will be an approximate answer, not an exact one. We can round to any place value of a multi-digit number by using the RULES OF ROUNDING. First, identify the place value being rounded and UNDERLINE the digit. Next, find the place value of the digit to the RIGHT and CIRCLE it. This number will tell us what we need to do. Now, look at these two place values. If the number you are rounding is followed by zero to four, the number being rounded STAYS THE SAME. If the number you are rounding is followed by five to nine, round the number UP to the NEXT NUMBER, because it is closer to the next whole number. Finally, all the remaining place values AFTER the rounded number are replaced with zeros. Sklyar sees a plane flying at thirty-eight thousand, five hundred and sixty feet. Let's help round to the nearest ten-thousands place to identify the approximate distance.

First, put our exact number in the place value chart and identify the place value we are rounding. We are rounding the ten-thousands place, so UNDERLINE the THREE. Next, find and circle the place value of the digit to the right, which is the eight in the thousands place. Because eight is between five and nine, this tells us to round UP. That means we change the ten thousands place to a four, and the following place values are replaced with zeros. Thirty-eight thousand, five hundred and sixty feet rounded to the nearest ten-thousand is FORTY-THOUSAND. "The plane was flying at approximately forty-thousand feet." Skylar looks into space and sees a satellite. The satellite is twenty-two thousand, two hundred and twenty-three miles away. We can round the distance of the satellite to the THOUSANDS place to get an approximate distance. We’ll put the exact number in the place value chart. First, identify the digit in the place value we are rounding and underline it. What do we underline? We underline the TWO in the THOUSANDS place. Now, circle the digit to the right, which is THIS two in the hundreds place. What does the two in the hundreds place tell us to do to the two in the thousands place? The two tells us the digit stays the same. The following place values will be replaced with zeros. Notice the digit in the TEN thousands place didn’t change. This is because it is BEFORE the place value we rounded. The satellite is approximately twenty-two thousand miles away. Skylar views the moon. It is two hundred and thirty-eight thousand, eight hundred and fifty-five miles away. We’ll round this distance to the HUNDREDS place to get a close approximation. First, put the number in the place value chart and underline the digit we are rounding. Which number do we underline? The eight in the HUNDREDS place. Now, circle the digit to the right. Which number do we circle? The five in the TENS place. As there is a five in the tens place, what does that tell us to do to the eight? Round UP to nine. What is the rounded number? Two hundred and thirty-eight thousand, NINE HUNDRED. The moon is approximately two hundred and thirty-eight thousand, nine hundred miles away. Skylar spots a UFO in the distance. While she tries to identify it, let's summarise. Remember, rounding numbers is a way of simplifying a number to make it easier to work with. We can round to any place value of a multi-digit number by using the RULES OF ROUNDING. First, identify the place value being rounded and UNDERLINE the digit. Next, find the place value of the digit to the right and CIRCLE it. If the number you are rounding is followed by five to nine, round the number up to the next number. If the number you are rounding is followed by zero to four, the number being rounded stays the same.

Is it a BIRD!? Is it a PLANE!? No, IT'S SUPER HENRY!

Rounding Multi-Digit Numbers 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.
  • Recognising place value.

    Hints

    Find and underline the 2 in each number and then match the correct place value.

    Here the 2 is in the ten-thousands column. This image can help you identify the other places.

    The short way of writing each place value:

    • O - ones
    • T - tens
    • H - hundreds
    • T - thousands
    • TT - ten-thousands
    • HT - hundred-thousands

    Solution

    Look at the place value charts above:

    • 231,874 is the number with 2 in the hundred-thousands place
    • 20,873 is the number with 2 in the ten-thousands place
    • 12,874 is the number with 2 in the thousands place
    • 45,821 is the number with 2 in the tens place
    • 801,472 is the number with 2 in the ones place

  • How to round to the nearest 10,000 (ten thousand).

    Hints

    The place value chart helps us to see the different place values. When rounding to the 10,000 place, we underline the digit in that place value and circle the digit to its right.

    If the thousand place has any of the digits 0-4, the digit in the ten-thousand place will stay the same.

    If the thousand place has any of the digits 5-9, the digit in the ten-thousand place will increase by one.

    Solution
    • To round 45,832 to the nearest 10,000, we underline the digit 4 because it is in the 10,000 place, and circle the digit 5 that is in the 1,000 place.
    • Since the circled digit is 5, the number 45,832 rounds up
    • 45,832 rounded to the nearest 10,000 is 50,000
    • Whereas the number, 42,832 rounded to the nearest 10,000 is 40,000.
  • Round up or stay the same?

    Hints

    The digit that will round up or stay the same is in the 100,000 place. Which place value will tell us what to do?

    If the telling digit is 0-4, the rounded digit will stay the same.

    If the telling digit is 5-9, the rounded digit will round up.

    Solution

    Rounding to the nearest 100,000

    • 147,892 stays the same because the digit 4 is 0-4, so this rounds to 100,000.
    • 352,146 rounds up because the digit 5 is 5-9, so this rounds to 400,000.
    • 678,093 rounds up because the digit 7 is 5-9, so this rounds to 700,000.
    • 921,503 stays the same because the digit 2 is 0-4, so this rounds to 900,000.
    • 501,872 stays the same because the digit 0 is 0-4, so this rounds to 500,000.

  • How have the numbers been rounded?

    Hints

    After rounding the digit that is being rounded, all the other place values after the rounded digit are replaced with zeros. Check out the example above when 38,712 is rounded to the nearest 10,000.

    The rounded place value comes just before the zeros.

    Solution
    • 700,000 is 728,819 rounded to the nearest 100,000.
    • 5,860 is 5,863 rounded to the nearest 10.
    • 730,000 is 728,819 rounded to the nearest 10,000.
    • 5,900 is 5,863 rounded to the nearest 100.
  • Round 12,438 to the nearest 10,000.

    Hints

    First, identify and underline the digit in the ten-thousands place.

    The digit, 2, in the thousand place lets us know that the 1 in the ten-thousands place should stay the same.

    Is 12,438 closer to 10,000 or 20,000?

    Solution

    12,438 rounds to 10,000.

    • The digit we are rounding is the 1 in the ten-thousands place.
    • The digit 2 in the 1,000 place tells us what to do. We need to round down because 2 is between 0-4.
    • The digit 1 in the ten-thousand place stays the same and all the other digits turn to zero.

  • Which numbers round to 156,000?

    Hints

    It is possible to get the same number when rounding different numbers. For example, 125 rounds up to 130 when rounding to the nearest 10, and 132 also rounds down to 130 when rounding the same place value.

    Find numbers that can round to 156,000 when rounding the 1,000 place.

    Solution
    • 157,321 does not round to 156,000 ❌
    • 155,812 does round to 156,000 ✅
    • 156,341 does round to 156,000 ✅
    • 156,782 does not round to 156,000 ❌
    • 155,389 does not round to 156,000 ❌
    • 156,911 does not round to 156,000 ❌
    • 156,282 does round to 156,000 ✅