Introduction

When we round a number to the nearest ten, we find the closest multiple of ten to our number.

For example, let's round the following number to the nearest ten:

123

We begin by drawing a number line:



Looking at the number line, the closest multiples of ten to 123 are 120 and 130.

Let's add these multiples of 10 to our diagram.



Now, since 123 is closer to {\color{DarkGreen}120} than {\color{SaddleBrown}130}, this is the number we round to.

Therefore, 123 rounded to the nearest ten is 120.

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Recognizing Multiples of 10 and 100

We can use the following rules to recognize multiples of 10 and 100{:}

  • Multiples of 10 always end in at least one zero.

    For example, all the following numbers are multiples of 10{:} 20, \qquad 80, \qquad 110, \qquad 200

  • Similarly, multiples of 100 always end in at least two zeros.

    For example, all the following numbers are multiples of 100{:} 100, \qquad 500, \qquad 2,100, \qquad 3,000

Let's look at an example of rounding up to the nearest 100.

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Example: Rounding Down Using a Number Line

Using the number line below, round 4,335 to the nearest hundred.

EXPLANATION

Rounding a number to the nearest hundred means finding the closest multiple of one hundred to our number.

The closest multiples of 100 to 4,335 are 4,300 and 4,400.

Let's add these multiples of 100 to our diagram.



Since 4,335 is closer to {\color{DarkGreen}4,300} than {\color{SaddleBrown}4,400}, this is the number we round to.



Therefore, 4,335 rounded to the nearest hundred is 4,300.

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Practice: Rounding Down Using a Number Line

Using the number line above, round $283$ to the nearest ten.

a
 $300$
b
 $290$
c
 $285$
d
 $273$
e
 $280$
Practice: Rounding Down Using a Number Line

Using the number line above, round $1,233$ to the nearest hundred.

a
 $1,250$
b
 $1,200$
c
 $1,300$
d
 $1,235$
e
 $1,500$
Rounding Down Whole Numbers Using Place Value Charts

We can round whole numbers using a place value chart.

To demonstrate, let's again round the following number to the nearest ten:

123

We start by writing our number's digits in a place value chart. Since we're rounding to the nearest ten, we highlight the tens place:

hundreds tens ones
1 2 3

We then look one digit to the right in the chart (i.e., the ones place) and compare it to the number 5{:}

hundreds tens ones
1 2 \bbox[2pt,Gainsboro]{\color{red}3}

Since \color{red}3 is less than 5 , we round down. To do this, we put \color{blue}0 in the ones place:

hundreds tens ones
1 2 \bbox[2pt,Gainsboro]{\color{blue}0}

And that's it!

Therefore, we conclude that 123 rounded to the nearest ten is 120.

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Example: Rounding Down to the Nearest Ten

Round 25,234 to the nearest ten.

EXPLANATION

We start by writing our number into a place value chart. Notice the tens place:

ten-thousands thousands hundreds tens ones
2 5 2 3 4

We then look one digit to the right in the chart (this will be the ones place) and compare it to the number 5{:}

ten-thousands thousands hundreds tens ones
2 5 2 3 \bbox[2pt,Gainsboro]{\color{red}4}

Since \color{red}4 is less than 5 , we round down. To do this, we put \color{blue}0 in the ones place:

ten-thousands thousands hundreds tens ones
2 5 2 3 \bbox[2pt,Gainsboro]{\color{blue}0}

Therefore, 25,234 rounded to the nearest ten is 25,230.

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Practice: Rounding Down to the Nearest Ten

Round $5,134$ to the nearest ten.

a
 $5,134$
b
 $5,000$
c
 $5,100$
d
 $5,140$
e
 $5,130$
Practice: Rounding Down to the Nearest Ten

Round $37,332$ to the nearest ten.

a
 $37,200$
b
 $37,320$
c
 $37,330$
d
 $37,232$
e
 $37,300$
Practice: Rounding Down to the Nearest Ten

Rounding $7,815,933$ to the nearest ten, we get

a
b
c
d
e
Rounding Down to Other Value Places

We can use a similar method to round whole numbers to the nearest hundred, thousand, ten-thousand, and so on.

For example, let's round 1,824 to the nearest hundred.

We start by writing our number into a place value chart. But this time, since we're rounding to the nearest hundred, we highlight the hundreds place:

thousands hundreds tens ones
1 8 2 4

We then look one digit to the right in the chart (this will be the tens place) and compare it to the number 5{:}

thousands hundreds tens ones
1 8 \bbox[2pt,Gainsboro]{\color{red}2} 4

Since \color{red}2 is less than 5 , we round down. To do this, we put \color{blue}0 in all places to the right of the hundreds (both tens and ones):

thousands hundreds tens ones
1 8 \bbox[2pt,Gainsboro]{\color{blue}0} \bbox[2pt,Gainsboro]{\color{blue}0}

Therefore, 1,824 rounded to the nearest hundred is 1,800.

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Example: Rounding Down to the Nearest Hundred

Round 200,238 to the nearest hundred.

EXPLANATION

We start by writing our number into a place value chart. Notice the hundreds place:

hundred-thousands ten-thousands thousands hundreds tens ones
2 0 0 2 3 8

We then look one digit to the right in the chart (this will be the tens place) and compare it to the number 5{:}

hundred-thousands ten-thousands thousands hundreds tens ones
2 0 0 2 \bbox[2pt,Gainsboro]{\color{red}3} 8

Since \color{red}3 is less than 5 , we round down. To do this, we put \color{blue}0 in all places to the right of the hundreds (into tens and ones):

hundred-thousands ten-thousands thousands hundreds tens ones
2 0 0 2 \bbox[2pt,Gainsboro]{\color{blue}0} \bbox[2pt,Gainsboro]{\color{blue}0}

Therefore, 200,238 rounded to the nearest hundred is 200,200.

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Practice: Rounding Down to the Nearest Hundred

Rounding $9,244$ to the nearest hundred, we get

a
b
c
d
e
Practice: Rounding Down to the Nearest Hundred

Rounding $127,847$ to the nearest hundred, we get

a
b
c
d
e
Practice: Rounding Down to the Nearest Hundred

Rounding $4,249,623$ to the nearest hundred, we get

a
b
c
d
e
Example: Rounding Down to the Nearest Thousand, Ten-Thousand, or Hundred-Thousand

Round 7,452 to the nearest thousand.

EXPLANATION

We start by writing our number into a place value chart. Notice the thousands place:

thousands hundreds tens ones
7 4 5 2

We then look one digit to the right in the chart (this will be the hundreds place) and compare it to the number 5{:}

thousands hundreds tens ones
7 \bbox[2pt,Gainsboro]{\color{red}4} 5 2

Since \color{red}4 is less than 5 , we round down. To do this, we put \color{blue}0 in all places to the right of the thousands (into hundreds, tens, and ones):

thousands hundreds tens ones
7 \bbox[2pt,Gainsboro]{\color{blue}0} \bbox[2pt,Gainsboro]{\color{blue}0} \bbox[2pt,Gainsboro]{\color{blue}0}

Therefore, 7,452 rounded to the nearest thousand is 7,000.

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Practice: Rounding Down to the Nearest Thousand, Ten-Thousand, or Hundred-Thousand

Rounding $5,217$ to the nearest thousand, we get

a
b
c
d
e
Practice: Rounding Down to the Nearest Thousand, Ten-Thousand, or Hundred-Thousand

Round $592,723$ to the nearest ten thousand.

a
 $580,000$
b
 $592,000$
c
 $600,000$
d
 $590,000$
e
 $593,000$
Practice: Rounding Down to the Nearest Thousand, Ten-Thousand, or Hundred-Thousand

Rounding $5,530,899$ to the nearest hundred thousand, we get

a
b
c
d
e
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