3.12: Decimal Rounding Given Place Value
Kalisha has a small bag that weighs 0.879 pounds. She is filling out a form that only allows her to write the weight to the hundredths. The form tells her to round to the nearest hundredths, but she doesn't know how to do that. How can she round 0.879 to the nearest hundredths, and what number should she write on the form?
In this concept, you will learn how to round to a given place value.
Rounding Decimals to a Given Place Value
You can use place value to help you round numbers to the nearest whole or tenths, hundredths, thousandths, etc.
Let's look at an example.
Round 0.345 to the nearest tenth.
To help you with this, put the number in the place value chart.
Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


.  3  4  5 
The 3 is in the tenths place. The 4 is the digit to the right of the tenths place. 4 is less than 5, so leave the 3 alone.
The answer is 0.3 is the nearest tenth.
You could have put zeros to represent the other digits, but that isn’t necessary.
Let's look at another example.
Round 0.567 to the nearest hundredth.
To help with this, let’s use the place value chart again.
Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


.  5  6  7 
The 6 is in the hundredths place. The 7 is the digit to the right of the hundredths place. Since 7 is 5 or greater, round up to the next digit. The 6 becomes a 7.
The answer is 0.57.
Notice that the five is included because it is to the left of the place you are rounding.
Examples
Example 1
Earlier, you were given a problem about Kalisha and her bag.
Round 0.879 to the nearest hundredths for her and write the value that she should put on the form.
First, put the number in the place value chart.
Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


.  8  7  9 
Next, determine if the number to the right of the hundredths place is 5 or greater.
Yes, it is greater.
Then, round the number in the hundredths place to the next value.
0.88
The answer is 0.88. Kalisha should write 0.88 on the form.
Example 2
Round 0.221 to the nearest tenth.
First, put the number in the place value chart.
Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


.  2  2  1 
Next, determine if the number to the right of the tenths place is 5 or greater.
No
Then, leave the number in the tenths place the same.
0.2
The answer is 0.2.
Example 3
Round 0.892 to the nearest tenth.
First, put the number in the place value chart.
Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


.  8  9  2 
Next, determine if the number to the right of the tenths place is 5 or greater.
Yes
Then, round the number in the tenths place to the next value.
0.9
The answer is 0.9.
Example 4
Round 0.632 to the nearest hundredth.
First, put the number in the place value chart.
Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


.  6  3  2 
Next, determine if the number to the right of the hundredths place is 5 or greater.
No
Then, round the number in the hundredths place to the next value.
0.63
The answer is 0.63.
Example 5
Round 0.1238 to the nearest thousandths.
First, put the number in the place value chart.
Tens  Ones  Tenths  Hundredths  Thousandths 
Ten Thousandths 


.  1  2  3  8 
Next, determine if the number to the right of the thousandths place is 5 or greater.
Yes
Then, round the number in the thousandths place to the next value.
0.124
The answer is 0.124.
Review
Round according to place value.
 Round .45 to the nearest tenth
 Round .67 to the nearest tenth
 Round .123 to the nearest tenth
 Round .235 to the nearest hundredth
 Round .567 to the nearest hundredth
 Round .653 to the nearest hundredth
 Round .2356 to the nearest thousandth
 Round .5672 to the nearest thousandth
 Round .8979 to the nearest thousandth
 Round .1263 to the nearest thousandth
 Round .056 to the nearest tenth
 Round .0091 to the nearest hundredth
 Round .0918 to the nearest tenth
 Round .0023 to the nearest thousandth
 Round .1368 to the nearest hundredth
Review (Answers)
To see the Review answers, open this PDF file and look for section 3.12.
Resources
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Decimal
In common use, a decimal refers to part of a whole number. The numbers to the left of a decimal point represent whole numbers, and each number to the right of a decimal point represents a fractional part of a power of onetenth. For instance: The decimal value 1.24 indicates 1 whole unit, 2 tenths, and 4 hundredths (commonly described as 24 hundredths).Round
To round is to reduce the number of nonzero digits in a number while keeping the overall value of the number similar.Image Attributions
In this concept, you will learn how to round to a given place value.
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