In this lesson, we'll extend our knowledge of rounding to situations where we must round up instead of down.
For example, let's round to the nearest ten:
We begin by drawing a number line and plotting our number.
Rounding a number to the nearest ten means finding the closest multiple of ten to our number.
The closest multiples of ten to are and Let's add these multiples of to our diagram:
Now, since is closer to than this is the number we round to.
Therefore, rounded to the nearest ten is
We can use the following rules to recognize multiples of and
Multiples of always end in at least one zero.
For example, all the following numbers are multiples of
Multiples of always end in at least two zeros.
For example, all the following numbers are multiples of
Let's look at an example of rounding up to the nearest
Using the number line below, round to the nearest hundred.
Rounding a number to the nearest hundred means finding the closest multiple of one hundred to our number.
The closest multiples of to are and
Let's add these multiples of to our diagram.
Since is closer to than this is the number we round to.
Therefore, rounded to the nearest hundred is
Using the number line above, round $287$ to the nearest ten.
|
a
|
$280$ |
|
b
|
$300$ |
|
c
|
$288$ |
|
d
|
$290$ |
|
e
|
$200$ |
Using the number line above, round $1,275$ to the nearest hundred.
|
a
|
$1,270$ |
|
b
|
$1,300$ |
|
c
|
$1,200$ |
|
d
|
$1,250$ |
|
e
|
$1,280$ |
We can also round whole numbers using place value charts.
To demonstrate, let's again round the following number to the nearest ten:
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 |
We then look one digit to the right in the chart (this will be the ones place) and compare it to the number
| hundreds | tens | ones |
Now, since is greater or equal to , we must round up. To do this, we follow two steps:
- We put into the ones place:
| hundreds | tens | ones |
- Then, we increase the tens value by one:
| hundreds | tens | ones |
Therefore, rounded to the nearest ten is
Round to the nearest ten.
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
| ten-thousands | thousands | hundreds | tens | ones |
Since is greater or equal to , we must round up. To do this, we follow two steps:
- We put into the ones place:
| ten-thousands | thousands | hundreds | tens | ones |
- Then, we increase the tens value by one:
| ten-thousands | thousands | hundreds | tens | ones |
Therefore, rounded to the nearest ten is
Round $276$ to the nearest ten.
|
a
|
$270$ |
|
b
|
$260$ |
|
c
|
$200$ |
|
d
|
$300$ |
|
e
|
$280$ |
Round $40,535$ to the nearest ten.
|
a
|
$41,000$ |
|
b
|
$40,540$ |
|
c
|
$40,530$ |
|
d
|
$40,600$ |
|
e
|
$40,500$ |
Round $1,002,109$ to the nearest ten.
|
a
|
$1,002,000$ |
|
b
|
$1,002,120$ |
|
c
|
$1,002,100$ |
|
d
|
$1,002,110$ |
|
e
|
$1,002,109$ |
We can round whole numbers to the nearest hundred, thousand, and so on.
For example, let's round to the nearest hundred.
We start by writing our number into a place value chart. And since we're rounding to the nearest hundred, we highlight the hundreds place:
| hundreds | tens | ones |
We then look one digit to the right in the chart (this will be the tens place) and compare it to the number
| hundreds | tens | ones |
Since is greater or equal to , we must round up. To do this, we follow two steps:
- We put into all places to the right of the hundreds (tens and ones):
| hundreds | tens | ones |
- Then, we increase the hundreds value by one:
| hundreds | tens | ones |
Therefore, rounded to the nearest hundred is
Round to the nearest thousand.
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
| thousands | hundreds | tens | ones |
Since is greater or equal to , we must round up. To do this, we follow two steps:
- We put into all places to the right of the thousands (into hundreds, tens, and ones):
| thousands | hundreds | tens | ones |
- Then, we increase the thousands value by one:
| thousands | hundreds | tens | ones |
Therefore, rounded to the nearest thousand is
Round $370,368$ to the nearest hundred.
|
a
|
$370,368$ |
|
b
|
$370,400$ |
|
c
|
$370,370$ |
|
d
|
$370,100$ |
|
e
|
$370,300$ |
Round $4,306,915$ to the nearest ten thousand.
|
a
|
$4,306,920$ |
|
b
|
$4,310,000$ |
|
c
|
$4,307,000$ |
|
d
|
$4,300,000$ |
|
e
|
$4,400,000$ |
Round $6,523,451$ to the nearest million.
|
a
|
$6,500,000$ |
|
b
|
$6,600,000$ |
|
c
|
$6,000,000$ |
|
d
|
$7,000,000$ |
|
e
|
$6,530,000$ |