Converting Decimals and Fractions

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Team Digital
Converting Decimals and Fractions
CCSS.MATH.CONTENT.4.NF.C.6

Content

Axel and Tank are on a walk when they see the Tricky Troll. The Tricky Troll asks for their help with converting fractions and decimals in exchange for some tickets to a big show! Let’s help with converting fractions to decimals and converting decimals to fractions so they can unlock the tickets!

Decimal Numbers and Decimal Fractions

A decimal number represents a part of a whole, like a fraction, but shows it slightly differently. A decimal fraction is a fraction with a denominator that is a power of ten, such as ten or one hundred. Next, let’s take a look at how to convert decimals to fractions.

How do I Convert a Decimal to a Fraction?

When converting decimals, ask yourself, “What is the place value of the last digit?”. If it is a tenth decimal place, then the denominator is ten. The numerator represents how many equal parts of a whole we have, which is the number you see in the tenth place in decimal. What is the tenth place in a decimal? Remember the tenths place is the first place value to the right of the decimal point. Let’s look at a tenth place decimal to try some converting decimals to fractions practice.

Below, we see one tenth as a decimal. In order to change or convert it into a fraction ask yourself, “What is the place value of the last digit?”. If it is a tenth decimal place, then the denominator is ten. The numerator represents how many equal parts of a whole we have, which is the number you see in the tenth place in decimal. 1 tenth as a decimal is equal to 1 tenth as a fraction. That means when converting tenths to decimals, the numerator one is in the tenths place.

How do I Convert a Fraction to a Decimal?

When converting fractions, ask yourself, “What is the place value represented in the denominator?”. If it is a hundredth decimal place, then the denominator is one hundred. The numerator represents how many equal parts of a whole we have, which is the number you see in the hundredth decimal. What is the hundredth place in a decimal? Remember the hundredth place is the second place value to the right of the decimal point. Let’s look at the hundredth decimal place to try converting a fraction to a decimal.

Below, we see one hundredth as a decimal. In order to change or convert it into a fraction ask yourself,“What is the place value represented in the denominator?”. If it is a hundredth decimal place, then the denominator is one hundred. The numerator represents how many equal parts of a whole we have, which is the number you see in the hundredth decimal place. One hundredth as a fraction is equal to one hundredth as a decimal.

Summary

When converting decimals, ask yourself, “What is the place value of the last digit?”. If it is a tenth decimal place, then the denominator is ten. The numerator represents how many equal parts of a whole we have, which is the number you see in the tenth place in decimal. When converting fractions, ask yourself, “What is the place value represented in the denominator?”. If it is a hundredth decimal place, then the denominator is one hundred. The numerator represents how many equal parts of a whole we have, which is the number you see in the hundredth decimal place.

Want some more converting fractions to decimals and converting decimals to fractions practice? You can find examples along with a converting fractions to decimals worksheet and a converting decimals to fractions worksheet on this website.

TranscriptConverting Decimals and Fractions

"And then my Mom was like, 'don't forget your turtleneck!', can you believe that!?" "Hi, can I help you?" "I need some help converting decimals and fractions to unlock these tickets for the big show tonight... if you help me, I'll give them to you." Let's help the Tricky Troll by... Converting Decimals and Fractions. A decimal number represents a part of a whole, like a fraction, but shows it slightly differently. We can convert, or change, decimal numbers into decimal fractions. A decimal fraction is a fraction with a denominator that is a power of ten, such as ten or one hundred. Here is the decimal number eight tenths represented using a base ten block. When converting decimal numbers into decimal fractions ask yourself: (...) What is the place value of the last digit? (...) Using a place value chart, we see the eight is in the TENTHS place... so the denominator is ten. The numerator, represents how many equal parts of a whole we have, which in this case is eight. Now that we have eight tenths in decimal notation AND fraction notation... what do you notice about them? (...) They are EQUIVALENT because they both represent eight parts of one whole... and we say eight-tenths for the fraction and the decimal! Now let's help the Tricky Troll by converting the decimal number thirty-five hundredths. When converting a decimal number into decimal fractions ask yourself: What is the place value of the last digit? (...) Using a place value chart, we see that the five is in the HUNDREDTHS place... so the denominator is one hundred. What is the numerator? (...) Thirty-five, since we have thirty-five parts of one whole. Thirty-five hundredths written as a decimal fraction is thirty-five OVER one hundred or "thirty-five hundredths". Last, we have the decimal fraction nine hundredths. This time, we are converting a decimal fraction into a decimal number. How can we convert this to a decimal number? (...) Since the denominator is one hundred, we know it is representing the HUNDREDTHS place value. How many hundredths do we have? (...) The numerator is nine, so write nine hundredths HERE in the place value chart. How many tenths do we have? (...) We don't have any tenths (...) so we write a zero in the TENTHS place. How many wholes do we have? (...) We don't any wholes so we write a zero in the ONES place. Nine hundredths written as a decimal number is zero POINT zero nine or "nine hundredths". We've converted all the decimals and fractions! While they get ready for the show, let's summarize. Remember (...) we can convert decimal fractions into decimal numbers and decimal numbers into decimal fractions. When converting decimal numbers into decimal fractions ask yourself... What is the place value of the last digit? The last place value is your denominator and... the numerator represents how many equal parts of a whole we have. When converting decimal fractions into decimal numbers... The denominator represents the place value and... the numerator represents how many equal parts of a whole we have. "I love Blue Troll Group!" "This is TURTALLY awesome!"

Converting Decimals and Fractions exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Converting Decimals and Fractions.
• What is the equivalent fraction?

Hints

Begin by writing the decimal onto a place value grid. Here, 0.8 is written on to the grid.

Identify the value of the digit by finding its position on the place value grid, an 8 in the tenths column means eight tenths.

To make a fraction that has a denominator of 100 into tenths, divide both the denominator and the numerator by 10. For example, $\frac{60}{100}$ ÷ 10 = $\frac{6}{10}$ which is the same as 0.6.

Solution

The equivalent fractions and decimals are:

• 0.2 = $\frac{2}{10}$ = $\frac{20}{100}$
• 0.5 = $\frac{5}{10}$
• 0.6 = $\frac{6}{10}$
• 0.8 = $\frac{8}{10}$
When we write 0.2 on a place value grid, there are zero ones and two tenths so we can say $\frac{2}{10}$. We can also write 0.20 meaning there are twenty hundredths, so we can also say $\frac{20}{100}$.

• How do we write fractions as decimals?

Hints

The denominator of the fraction is 100, so the numbers need to go as far as the hundredths column of the place value grid.

There are no ones in $\mathbf{\frac{75}{100}}$ so there will be no ones in the ones column of the place value grid.

Solution

$\mathbf{\frac{75}{100}}$ is made up of 7 tenths and 5 hundredths, or 75 hundredths, so there will be a 7 in the tenths column and a 5 in the hundredths column.

• Representing numbers.

Hints

Look how many parts there are in total, this is the denominator. How many parts are shaded? This is the numerator.

Once you know the fraction out of ten or one hundred, write this onto a place value grid. For example, 25 hundredths would be written as 0.25.

Simplify the fraction you are trying to find, to find an equivalent fraction. For example, 0.25 is the same as $\frac{25}{100}$ and would be simplified to $\frac{1}{4}$.

Solution
• The first image shows 5 parts out of 10 shown. This is the same as a half or fifty out of one hundred.
• The second image shows 75 parts shaded out of 100. This is the same as seventy five out of one hundred or zero point seven five.
• The third image shows 30 parts out of 100 or 3 out of ten. This is the same as zero point three, thirty hundredths or three tenths.
• Order the fractions and decimals.

Hints

Begin by converting all the amounts into the same value. You could make every amount into hundredths.

To convert $\frac{7}{10}$ to hundredths, multiply the numerator and denominator by ten to get $\frac{70}{100}$.

To convert a decimal into hundredths, write the decimal onto a place value grid. For example, 0.08 would have zero ones, zero tenths and eight hundredths ($\frac{8}{100}$).

Try drawing a hundred square and shading in the amount shown in the numerator when the denominator is 100, then see which fraction has the most shaded in.

Solution

The correct order from smallest to greatest values is:

• 0.04 or $\frac{4}{100}$. 0.04 is equivalent to zero ones, zero tenths and four hundredths.
• 0.2 or $\frac{20}{100}$. 0.2 is equivalent to zero ones and two tenths which is equivalent to twenty hundredths.
• $\mathbf{\frac{4}{10}}$ or $\frac{40}{100}$.
• 0.48 or $\frac{48}{100}$. 0.48 is equivalent to zero ones, four tenths and eight hundredths which is the same as forty-eight hundredths.
• $\mathbf{\frac{63}{100}}$
• $\mathbf{\frac{7}{10}}$ or $\frac{70}{100}$

• Find the fraction to match.

Hints

When we write 0.03 onto a place value grid, how many hundredths are there?

Can you find a fraction that has 100 as the denominator?

Solution

0.03 = $\mathbf{\frac{3}{100}}$. When we write the decimal onto a place value grid we can see that there are zero ones, zero tenths and three hundredths.

• Converting fractions to decimals.

Hints

To convert a fraction to a decimal, first convert the fraction so that it has a denominator of 10 or 100. To convert $\frac{6}{20}$, we can divide the numerator and denominator by 2 to get $\frac{3}{10}$.

Once the fraction is written as out of 10 or 100, write it on to a place value grid. $\frac{3}{10}$ has zero ones, 3 tenths and zero hundredths, so is equivalent to 0.3.

When a fraction has 5 as a denominator, multiply both the numerator and denominator by two so that the fraction is out of 10.

Solution
1. $\frac{35}{100}$ = 0.35 ✅
2. $\frac{2}{10}$ = 0.02 ❌ $\frac{2}{10}$ = 0.2
3. $\frac{3}{5}$ = 0.3 ❌ $\frac{3}{5}$ = 0.6
4. $\frac{4}{5}$ = 0.8 ✅
5. $\frac{12}{20}$ = 0.6 ✅
6. $\frac{2}{20}$ = 0.2 ❌ $\frac{2}{20}$ = 0.1
7. $\frac{7}{100}$ = 0.07 ✅
8. $\frac{1}{5}$ = 0.5 ❌ $\frac{1}{5}$ = 0.2