Introduction

When rounding whole numbers to the nearest ten, we sometimes need to adjust the hundreds, tens, and ones.

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

298

As usual, we start by writing our number into a place value chart, highlighting the tens place:

hundreds tens ones
2 9 8

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

hundreds tens ones
2 9 \bbox[2pt,Gainsboro]{\color{red}8}

Since \color{red}8 is greater or equal to 5 , we must round up. To do this, we follow the usual algorithm:

  • We put \color{blue}0 in the ones place and increase the tens value by one:
hundreds tens ones
2 9\bbox[2pt,Gainsboro]{\color{blue}+1} \bbox[2pt,Gainsboro]{\color{blue}0}
  • However, 9+1=10 tens is the same as 1 hundred and 0 tens. So, we must write 0 in the tens place and increase the number of hundreds by one:
hundreds tens ones
\bbox[2pt,Gainsboro]{\color{blue}3} \bbox[2pt,Gainsboro]{\color{blue}0} 0

Therefore, 298 rounded to the nearest ten is 300.

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Example: Rounding to the Nearest Ten

Round 311,695 to the nearest ten.

EXPLANATION

We start by writing our number into a place value chart, highlighting the tens place:

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

hundred-thousands ten-thousands thousands hundreds tens ones
3 1 1 6 9 \bbox[2pt,Gainsboro]{\color{red}5}

Since \color{red}5 is greater or equal to 5 , we must round up. To do this, we follow two steps:

  • We put \color{blue}0 in the ones place and increase the tens value by one:
hundred-thousands ten-thousands thousands hundreds tens ones
3 1 1 6 9\bbox[2pt,Gainsboro]{\color{blue}+1} \bbox[2pt,Gainsboro]{\color{blue}0}
  • However, 9+1=10 tens is the same as 1 hundred and 0 tens. So, we must write 0 in the tens place and increase the number of hundreds by one:
hundred-thousands ten-thousands thousands hundreds tens ones
3 1 1 \bbox[2pt,Gainsboro]{\color{blue}7} \bbox[2pt,Gainsboro]{\color{blue}0} 0

Therefore, 311,695 rounded to the nearest ten is 311,700.

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Practice: Rounding to the Nearest Ten

Round $497$ to the nearest ten.

a
 $510$
b
 $500$
c
 $499$
d
 $490$
e
 $400$
Practice: Rounding to the Nearest Ten

Round $12,396$ to the nearest ten.

a
 $12,390$
b
 $12,410$
c
 $13,000$
d
 $12,400$
e
 $12,300$
Example: Rounding to Some Other Place Value

Round 9,821 to the nearest thousand.

EXPLANATION

We start by writing our number into a place value chart, highlighting the thousands place:

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
9 \bbox[2pt,Gainsboro]{\color{red}8} 2 1

Since \color{red}8 is greater or equal to 5 , we must round up. To do this, we follow two steps:

  • We put \color{blue}0 in all places to the right of the thousands (into hundreds, tens, and ones) and increase the thousands value by one:
thousands hundreds tens ones
9\bbox[2pt,Gainsboro]{\color{blue}+1} \bbox[2pt,Gainsboro]{\color{blue}0} \bbox[2pt,Gainsboro]{\color{blue}0} \bbox[2pt,Gainsboro]{\color{blue}0}
  • However, 9+1=10 thousands is the same as 1 ten thousand and 0 thousands. So, we must write 0 in the thousands place and increase the number of ten-thousands by one:
ten-thousands thousands hundreds tens ones
\bbox[2pt,Gainsboro]{\color{blue}1} \bbox[2pt,Gainsboro]{\color{blue}0} 0 0 0

Therefore, 9,821 rounded to the nearest thousand is 10,000.

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Practice: Rounding to Some Other Place Value

Round $3,971$ to the nearest hundred.

a
 $3,970$
b
 $4,100$
c
 $4,000$
d
 $3,800$
e
 $3,900$
Practice: Rounding to Some Other Place Value

Round $2,329,662$ to the nearest thousand.

a
 $3,000,000$
b
 $2,329,700$
c
 $2,400,000$
d
 $2,330,000$
e
 $2,329,000$
Example: Rounding Up the Digit Nine Twice

Round 2,997,523 to the nearest ten thousand.

EXPLANATION

We start by writing our number into a place value chart, highlighting the ten-thousands place:

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

millions hundred-thousands ten-thousands thousands hundreds tens ones
2 9 9 \bbox[2pt,Gainsboro]{\color{red}7} 5 2 3

Since \color{red}7 is greater or equal to 5 , we must round up. To do this, we follow three steps:

  • We put \color{blue}0 in all places to the right of the ten-thousands (into thousands, hundreds, tens, and ones) and increase the ten-thousands value by one:
millions hundred-thousands ten-thousands thousands hundreds tens ones
2 9 9\bbox[2pt,Gainsboro]{\color{blue}+1} \bbox[2pt,Gainsboro]{\color{blue}0} \bbox[2pt,Gainsboro]{\color{blue}0} \bbox[2pt,Gainsboro]{\color{blue}0} \bbox[2pt,Gainsboro]{\color{blue}0}
  • However, 9+1=10 ten-thousands is the same as 1 hundred thousand and 0 ten-thousands. So, we must write 0 in the ten-thousands place and increase the number of hundred-thousands by one:
millions hundred-thousands ten-thousands thousands hundreds tens ones
2 9\bbox[2pt,Gainsboro]{\color{blue}+1} \bbox[2pt,Gainsboro]{\color{blue}0} 0 0 0 0
  • But, 9+1=10 hundred-thousands is the same as 1 million and 0 hundred-thousands. So, we must write 0 in the hundred-thousands place and increase the number of millions by one:
millions hundred-thousands ten-thousands thousands hundreds tens ones
\bbox[2pt,Gainsboro]{\color{blue}3} \bbox[2pt,Gainsboro]{\color{blue}0} 0 0 0 0 0

Therefore, 2,997,523 rounded to the nearest ten thousand is 3,000,000.

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Practice: Rounding Up the Digit Nine Twice

Round $201,995$ to the nearest ten.

a
 $201,000$
b
 $201,995$
c
 $201,900$
d
 $201,990$
e
 $202,000$
Practice: Rounding Up the Digit Nine Twice

Round $99,625$ to the nearest thousand.

a
 $99,000$
b
 $101,000$
c
 $100,000$
d
 $99,600$
e
 $98,000$
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