# Decimals Greater than 1 as Fractions

Content Decimals Greater than 1 as Fractions
Rating

Ø 3.9 / 9 ratings
The authors
Team Digital
Decimals Greater than 1 as Fractions
CCSS.MATH.CONTENT.4.NF.C.6

## Decimals Greater Than 1

When we have a number that is greater than 1 and written as a decimal, we can convert it so that it is written as a fraction. To write decimals greater than one as fractions, it is important to identify the place value for decimals greater than 1. This helps to know what the denominator is. Let’s look at the number one and fifty-seven hundredths as an example.

## Decimals Greater Than 1 as Fractions

The first step is to set up a place value chart to the hundredths place, and write the number on the place value chart. This means one goes in the ones place, five goes in the tenths place, and seven goes in the hundredths place.

Next, we write all the numbers as a fraction. One whole as a fraction is one over one. Five tenths as a fraction is five over ten, and seven hundredths as a fraction is seven over one hundred.

Then, we need to convert the fractions to have common, or the same, denominators. In this example, we will convert all fractions to have the denominator one hundred. We multiply the numerator and denominator by one hundred for one over one to get one hundred over one hundred. Then, we multiply the numerator and denominator by ten for five over ten to get fifty over one hundred. Seven over one hundred does not need converting.

Now, we add all the fractions together. The denominator remains one hundred, and we add one hundred plus fifty plus seven to give us one hundred and fifty-seven for the numerator.

Since one hundred and fifty-seven is greater than one hundred, it is an improper fraction. We can rewrite this as the mixed fraction, one and fifty-seven over one hundred.

This means that one and fifty-seven hundredths as a fraction is one and fifty-seven over one hundred.

## Decimals Greater Than 1 – Summary

Decimals greater than 1 are numbers greater than one with a decimal place. You can display decimals greater than 1 as fractions or as mixed numbers. When you need to represent numbers with decimals, you can use a place value chart to the hundredths place or multiply the number by 100. Follow these steps to identify the place value of decimals:

Step # What to do
1 Set up a place value chart to the hundredths
place and write down the number.
2 Write all the numbers as a fraction.
One whole is one over one as a fraction.
3 Convert the fractions to have common
4 Since the numerator will be greater than one hundred,
you can rewrite the fraction as a mixed number.

After watching the video you will find more interactive exercises, worksheets and further activities concerning decimals greater than 1. Use these to practice converting decimals greater than one to fractions.

### TranscriptDecimals Greater than 1 as Fractions

"Thanks for the help, Michelle." "Basically, we need to convert the decimals on your lock screen to fractions to unlock it!" "I just want to use my new shell phone." Let's help Axel unlock Tanks new shell phone by learning all about decimals greater than one as fractions. Decimals represent a whole number and a fractional part of a whole number. Decimals greater than one can be converted, or changed, into decimal fractions. Decimal fractions have a multiple of ten for the denominator, such as ten or one hundred. Let's look at the first decimal number to unlock Tank's new shell phone. We have one and fifty-seven hundredths. When converting decimal numbers to fractions, first, write each place value as a fraction. The ones place value is one over one, since it represents one whole. For the tenths place, write the decimal fraction five tenths, because it represents five equal parts of a whole divided into ten. For the hundredths place, write the decimal fraction seven hundredths, because it represents seven equal parts of a whole divided into one hundred. Next, convert to fractions with like denominators so the sum can be found. Convert all fractions to hundredths, the greatest denominator here. One over one becomes one hundred hundreths by multiplying the numerator and denominator by one hundred. Five tenths becomes fifty hundredths, by multiplying the numerator and denominator by ten. Seven hundredths already has one hundred for a denominator, so bring it down. Next, find the sum. The denominator stays one hundred. The sum of one hundred plus fifty plus seven, is one hundred fifty-seven. Convert to the mixed number one and fifty-seven over one hundred. One and fifty-seven hundredths is the same as one and fifty-seven over one hundred. Now the first code has been entered, let's look at the other code. The decimal number is three and four tenths. What is the first step? Write each place value as a fraction. Three as a fraction is three over one, and four tenths as a fraction is four tenths. What is the second step? Convert the fractions to fractions with like denominators. Since ten is the greatest denominator, convert the fractions to a denominator of ten. Three over one becomes thirty tenths, because we multiply the numerator and denominator by ten. And four tenths remains the same. What is the final step? Find the sum of the fractions. The denominator remains ten. Thirty plus four is thirty-four. Thirty-four tenths as a mixed number is three and four-tenths. Simplify further to three and two fifths by dividing the numerator and denominator by two. Three and four tenths is the same as three and two fifths! While Tank enters the last code to unlock his shell phone, let's review! Remember, to convert decimals greater than one to fractions, first, write each place value as a fraction. Second, convert the fractions to fractions with like denominators. Third, find the sum and simplify if needed. "And then my Mom was like, 'don't forget your turtleneck!', can you believe that?" "Oh boy, here we go...."

## Decimals Greater than 1 as Fractions exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Decimals Greater than 1 as Fractions.
• ### What does a decimal represent?

Hints

Decimals can be greater than one.

Decimals and fractions represent the same number, but in different forms.

Solution

A decimal represents a whole number and a fractional part of a whole number. We use decimals when counting money and measuring objects, so it is important to understand what they represent.

• ### What are the steps needed in order to convert a decimal greater than 1 to a fraction?

Hints

In this example, the decimals have been converted to fractions. 1.1 goes to the tenths place, so we write the fraction over 10. 1.11 goes to the hundredths place, so we write the fraction over 100.

Like means the same. So, in this example, the fractions were changed to all have the same denominator of 100.

Solution

The steps to converting a decimal greater than one to a fraction are as follows:

1. Write the decimal in the place value chart.
2. Write each place value as a fraction.
3. Convert the fractions so they have a like denominator.
4. Find the sum and simplify if needed.

• ### Which equation best represents the decimal 4.23?

Hints

Remember to find the greatest denominator and convert the other fractions to have the same denominator.

This example shows you how to write each place as a fraction.

Convert all fractions to the greatest denominator. In this example, the greatest denominator is 100.

Solution

The correct answer is $\frac{400}{100}$ + $\frac{20}{100}$ + $\frac{3}{100}$ = $\frac{423}{100}$. This simplifies to 4 $\frac{23}{100}$

As you can see in the picture, all the fractions need to have a denominator of 100 because it is the greatest. You convert each fraction to have a denominator of 100 by multiplying them by a multiple of ten. Once you do that, you can add the numerator of each fraction together to get your answer.

• ### Match the decimal to the fraction.

Hints

Decimals can be converted to fractions that have a denominator of ten. In this example the denominator is 100 which is a multiple of ten. So you change the original fractions to fractions over 100.

In the example, you can see that the decimal has been expanded into the chart by place value. We then use this chart to create fractions.

Decimals greater than one are going to be a mixed number. This means there will be a whole number and a fractional part like 2 $\frac{1}{2}$.

Solution

The matches are:

1. 2.67 and $\frac{267}{100}$
2. 5.6 and $\frac{560}{100}$
3. 7.8 and $\frac{78}{10}$
4. 4.25 and $\frac{425}{100}$
In order to match the pairs correctly, you had to use place value. Each match is based on ten. So if the decimal goes to the tenths place, the fraction will also have a denominator of ten. If the decimals goes to the hundredths place, the fraction will have a denominator of one hundred.

• ### Expand and convert the decimal 2.97.

Hints

When looking at a number, do we read it left to right or right to left?

The tenths column means the fraction is out of 10 and the hundredths column means the fraction is out of 100.

In the decimal 6.5, the 5 is in the tenths place because it represents $\frac{5}{10}$.

Solution

The position of the number tells its value, e.g. the 2 represents two ones, the 9 is in the tenths place so represents $\frac{9}{10}$, and the 7 is in the hundredths place so represents $\frac{7}{100}$.

You then have to convert the decimal to fractions which looks like this: $\frac{2}{1}$ $\frac{9}{10}$ $\frac{7}{100}$

• ### Match the place value chart to the equations.

Hints

Write the decimal onto a place value chart to find how many ones, tenths and hundredths it is made up of.

When the fractions are added, convert an improper fraction to a mixed number, e.g. $\frac{54}{10} = 5\frac{4}{10}$.

Solution

We use place value to expand decimals and think about the digits and their values.

Let's take a closer look at the first decimal. 6.7 is $\frac{60}{10}$ + $\frac{7}{10}$ which equals $\frac{67}{10}$ This is equivalent to 6 wholes and 7 tenths. This same concept applies to the rest of the problems.

1. 8.43 is $\frac{800}{100}$ + $\frac{40}{100}$ + $\frac{3}{100}$
2. 1.25 is $\frac{100}{100}$ + $\frac{20}{100}$ + $\frac{5}{100}$
3. 3. 6 is $\frac{30}{10}$ + $\frac{6}{10}$
4. 4.5 is $4\frac{5}{10}$
5. 4.05 is $4\frac{5}{100}$