Suppose we want to round 374.6 to the nearest whole number.

First, we locate the digit in the ones place:

37{\color{blue}{4}}.6

We then look one digit to the right and compare it to the number 5\mathbin{:}

37{\color{blue}{4}}.\!{\color{red}{6}}

Since \color{red}6 is greater than (or equal to) 5 , we must round up. To do this, we follow two steps:

  • First, we remove all of the digits to the right of the ones place: 374.6 \rightarrow 374

  • Then, we increase the value of the last digit by one:

374 \rightarrow 375

Therefore, 374.6 rounded to the nearest whole number is 375.

FLAG

437.67 rounded to the nearest whole number is

EXPLANATION

Rounding a decimal to the nearest whole number means finding the closest whole number to the original decimal.

We start by locating the digit in the ones place:

43{\color{blue}{7}}.67

We then look one digit to the right and compare it to the number 5\mathbin{:}

43{\color{blue}{7}}.\!{\color{red}{6}}7

Since \color{red}6 is greater than (or equal to) 5 , we must round up. To do this, we follow two steps:

  • First, we remove all digits to the right of the decimal point: 437.67 \rightarrow 437

  • Then, we increase the value of the last digit by one: 437 \rightarrow 438

Therefore, 437.67 rounded to the nearest whole number is 438.

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What is $52.8$ rounded to the nearest whole number?

a
$50$
b
$52$
c
$60$
d
$53$
e
$58$

$258.515$ rounded to the nearest whole number is

a
$260$
b
$255$
c
$258$
d
$259$
e
$257$

What is 14.65 rounded to the nearest tenth?

EXPLANATION

We start by locating the digit in the tenths place: 14.{\color{blue}{6}}5

We then look one digit to the right and compare it to the number 5\mathbin{:} 14.{\color{blue}{6}}{\color{red}{5}}

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

  • First, we remove all of the digits to the right of the tenths place: 14.65 \rightarrow 14.6

  • Then, we increase the value of the last digit by one: 14.6 \rightarrow 14.7

Therefore, 14.65 rounded to the nearest tenth is 14.7.

FLAG

What is $973.48$ rounded to the nearest tenth?

a
$973.3$
b
$973.2$
c
$973.8$
d
$973.4$
e
$973.5$

What is $1.317$ rounded to the nearest hundredth?

a
$1.31$
b
$1.35$
c
$1.3$
d
$1.4$
e
$1.32$

Sometimes, the digit in the place we are rounding to is 9. If we round up, increasing this digit by one makes 10. So, what do we do?

The answer is to replace 9 with the 0 and increase the next digit by one.

To illustrate, let's round 62.96 to the nearest tenth. We start by locating the digit in the tenths place: 62.{\color{blue}{9}}6

We then look one digit to the right and compare it to the number 5\mathbin{:} 62.{\color{blue}{9}}{\color{red}{6}}

Since \color{red}6 is greater than (or equal to) 5 , we round up. To do this, we follow two steps:

  • First, we remove all of the digits to the right of the tenths place: 62.96 \rightarrow 62.9

  • Then, because the last digit is a 9, we turn it into a 0 and increase the next digit by one: 62.9 \rightarrow 63.0

Therefore, 62.96 rounded to the nearest tenth is 63.0.

FLAG

What is 51.298 rounded to the nearest hundredth?

EXPLANATION

We start by locating the digit in the hundredths place:

51.2{\color{blue}{9}}8

We then look one digit to the right and compare it to the number 5\mathbin{:}

51.2{\color{blue}{9}}{\color{red}{8}}

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

  • First, we remove all of the digits to the right of the hundredths place: 51.298 \rightarrow 51.29

  • Then, because the last digit is a 9, we turn it into a 0 and increase the next digit by one:

51.29 \rightarrow 51.30

Therefore, 51.298 rounded to the nearest hundredth is 51.30.

FLAG

What is $369.6$ rounded to the nearest whole number?

a
$371$
b
$390$
c
$370$
d
$360$
e
$369$

The number $13.99$ rounded to the nearest tenth is

a
$13.9$
b
$14.1$
c
$13.0$
d
$14.0$
e
$14.8$

What is $9.996$ rounded to the nearest hundredth?

a
$10.90$
b
$20.00$
c
$19.00$
d
$10.00$
e
$9.99$

Some decimals have digits that continue forever.

For example, the number e, known as Euler's constant, is a very important number in mathematics. Its digits continue forever, which we denote using \ldots as follows:

e = 2.718\,\ldots\,.

Let's round this number to the nearest hundredth.

First, we locate the digit in the hundredths place: 2.7{\color{blue}{1}}8 \ldots

We then look one digit to the right and compare it to the number 5\mathbin{:} 2.7{\color{blue}{1}}{\color{red}{8}} \ldots

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

  • First, we remove all of the digits to the right of the hundredths place: 2.718 \ldots \rightarrow 2.71

  • Then, we increase the value of the last digit by one: 2.71 \rightarrow 2.72

Therefore, 2.718 \ldots rounded to the nearest hundredth is 2.72.

FLAG

What is 36.87 \ldots rounded to the nearest tenth?

EXPLANATION

First, we locate the digit in the tenths place: 36.{\color{blue}{8}}7 \ldots

We then look one digit to the right and compare it to the number 5\mathbin{:} 36.{\color{blue}{8}}{\color{red}{7}} \ldots

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

  • First, we remove all of the digits to the right of the tenths place: 36.87 \ldots \rightarrow 36.8

  • Then, we increase the value of the last digit by one: 36.8 \rightarrow 36.9

Therefore, 36.87 \ldots rounded to the nearest tenth is 36.9.

FLAG

$231.6 \ldots$ rounded to the nearest whole number is

a
$231$
b
$232$
c
$235$
d
$230$
e
$233$

What is $0.281 \ldots$ rounded to the nearest tenth?

a
$0.8$
b
$1.0$
c
$0.1$
d
$0.2$
e
$0.3$

The number $9.198 \ldots$ rounded to the nearest hundredth is

a
$9.20$
b
$9.10$
c
$9.30$
d
$9.21$
e
$9.19$
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