Introduction

When we round a decimal to the nearest whole number, we find the closest whole number to the original decimal.

For example, let's consider the following decimal:

16.4

To round 16.4 to the nearest whole number, we first identify the digit in the ones place: 1{\color{blue}{6}}.4

We then look one digit to the right and compare it to the number 5\mathbin{:} 1{\color{blue}{6}}.\!{\color{red}{4}}

Since \color{red}4 is less than 5 , we round down. To do this, we remove all the digits to the right of the decimal point:

16.4 \rightarrow 16

Therefore, 16.4 rounded to the nearest whole number is 16.

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Example: Rounding a Decimal to the Nearest Whole Number

What is 8.31 rounded to the nearest whole number?

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:

{\color{blue}{8}}.31

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

{\color{blue}{8}}.\!{\color{red}{3}}1

Since \color{red}3 is less than 5 , we round down. To do this, we remove all the digits to the right of the decimal point:

8.31 \rightarrow 8

Therefore, 8.31 rounded to the nearest whole number is 8.

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Practice: Rounding a Decimal to the Nearest Whole Number

What is $3.4$ rounded to the nearest whole number?

a
 $0$
b
 $5$
c
 $2$
d
 $3$
e
 $4$
Practice: Rounding a Decimal to the Nearest Whole Number

$33.23$ rounded to the nearest whole number is

a
 $34$
b
 $30$
c
 $32$
d
 $33$
e
 $35$
Rounding to Other Decimal Places

We can round a decimal to any place, such as the nearest tenth or nearest hundredth. The process is almost the same as rounding a decimal to the nearest whole number.

To illustrate, let's round 8.31 to the nearest tenth. We start by locating the digit in the tenths place:

8.{\color{blue}{3}}1

We then look one digit to the right and compare it to the number 5\mathbin{:} 8.{\color{blue}{3}}{\color{red}{1}}

Since \color{red}1 is less than 5 , we round down. To do this, we remove all the digits to the right of the tenths place:

8.31 \rightarrow 8.3

Therefore, 8.31 rounded to the nearest tenth is 8.3.

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Example: Rounding a Decimal to the Nearest Tenth

What is 76.11 rounded to the nearest tenth?

EXPLANATION

We start by locating the digit in the tenths place:

76.{\color{blue}{1}}1

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

76.{\color{blue}{1}}{\color{red}{1}}

Since \color{red}1 is less than 5 , we round down. To do this, we remove all the digits to the right of the tenths place:

76.11 \rightarrow 76.1

Therefore, 76.11 rounded to the nearest tenth is 76.1.

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Practice: Rounding a Decimal to the Nearest Tenth

$8.71$ rounded to the nearest tenth is

a
 $8.6$
b
 $9.0$
c
 $8.8$
d
 $8.7$
e
 $8.5$
Practice: Rounding a Decimal to the Nearest Tenth

$537.834$ rounded to the nearest tenth is

a
 $538.0$
b
 $537.9$
c
 $537.8$
d
 $537.0$
e
 $537.7$
Example: Rounding a Decimal to the Nearest Hundredth

What is 2.343 rounded to the nearest hundredth?

EXPLANATION

We start by locating the digit in the hundredths place:

2.3{\color{blue}{4}}3

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

2.3{\color{blue}{4}}{\color{red}{3}}

Since \color{red}3 is less than 5 , we round down. To do this, we remove all the digits to the right of the hundredths place:

2.343 \rightarrow 2.34

Therefore, 2.343 rounded to the nearest hundredth is 2.34.

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Practice: Rounding a Decimal to the Nearest Hundredth

What is $628.731$ rounded to the nearest hundredth?

a
 $628.74$
b
 $629.00$
c
 $628.73$
d
 $628.00$
e
 $628.70$
Practice: Rounding a Decimal to the Nearest Hundredth

$0.841$ rounded to the nearest hundredth is

a
 $1$
b
 $0.85$
c
 $0.9$
d
 $0.84$
e
 $0.8$
Decimal Digits That Continue Forever

Some decimals have digits that continue forever.

For example, the number \pi, pronounced "pie," is a very important number in mathematics. Its digits continue forever, which we denote using \ldots as follows:

\pi= 3.141\,\ldots\,.

Let's round this number to the nearest hundredth.

First, we locate the digit in the hundredths place: 3.1{\color{blue}{4}}1 \ldots

We then look one digit to the right and compare it to the number 5\mathbin{:} 3.1{\color{blue}{4}}{\color{red}{1}} \ldots

Since \color{red}1 is less than 5 , we round down. To do this, we remove all digits to the right of the hundredths place:

3.141\ldots \rightarrow 3.14

Therefore, \pi = 3.141\ldots rounded to the nearest hundredth is 3.14.

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Example: Rounding a Decimal Whose Digits Continue Forever

What is 3.842 \ldots rounded to the nearest tenth?

EXPLANATION

We start by locating the digit in the tenths place:

3.{\color{blue}{8}}42\ldots

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

3.{\color{blue}{8}}{\color{red}{4}}2 \ldots

Since \color{red}4 is less than 5 , we round down. To do this, we remove all the digits to the right of the tenths place:

3.842 \ldots \rightarrow 3.8

Therefore, 3.842 \ldots rounded to the nearest tenth is 3.8.

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Practice: Rounding a Decimal Whose Digits Continue Forever

$12.63 \ldots$ rounded to the nearest tenth is

a
 $12.6$
b
 $12.7$
c
 $12.0$
d
 $13.0$
e
 $12.5$
Practice: Rounding a Decimal Whose Digits Continue Forever

$16.431 \ldots$ rounded to the nearest whole number is

a
 $20$
b
 $16$
c
 $10$
d
 $18$
e
 $17$
Practice: Rounding a Decimal Whose Digits Continue Forever

$0.751 \ldots$ rounded to the nearest hundredth is

a
 $0.80$
b
 $0.70$
c
 $0.76$
d
 $0.74$
e
 $0.75$
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