Converting Between Decimals and Fractions

Do you remember what decimals are?

**Decimals **are numbers that express whole numbers and fractions. A **decimal point **separates the values for whole numbers and fractions.Β

This is an example of a decimal.

0.25

Let's use a **place value chart**.

This decimal **does not have a whole number **because we have 0 in the Ones place.

The value of this decimal is **less than 1.**

π The definition of decimals tells us that there is a connection between decimals and fractions.Β

π We can turn any **decimal **into a **fraction,** and any fraction into a decimal.

The digits to the right of a decimal point **show values that are less than 1**.

Look at this example:

0.1

π The first digit to the right of the decimal point** **has a place value of 1/10.

We see that digits to the **right **π of **decimal points **show values for **fractions.**Β

The value of a digit depends on where it's placed.

Look at this decimal.

**2** is in the **Tenths place.**

The **Tenths place **shows us how many tenths we're dealing with.

In fraction form, a tenth is written as **1/10.**

For our example, how many tenths are there?

β
Yes, 2 tenths. We write this as **2/10.**

**5 **is in the **Hundredths place.**

The **Hundredths place **shows us how many hundredths we're dealing with.

In fraction form, a hundredth is written as **1/100.**

How many hundredths does our example show?

β
5 Hundredths! We write this as **5/100.**

** **Tip: As we **move further to the right **of a decimal number, the **values of the digits become smaller and smaller. **We can have thousandths, ten thousandths, etc.

Let's convert this decimal to a fraction:

0.25

We have to follow 2 steps.

**Step 1. ****Figure out the value of each digit**.** **

**β
2 **is in the Tenths place. It is **2/10.**

**β
5 **is in the Hundredths place. It is **5/100**.

**Step 2. ****Add the fractions together**.

We need to have the same denominators (the numbers at the bottom) when adding fractions.

π We do this by finding the **greatest denominator.**

Of the two denominators, which is the greatest, or biggest?

β It's 100!

π So, we have to convert **2/10** by multiplying it by **10/10.** This creates an **equivalent fraction **that's easier to work with, but has the same value!

Now, we can add because our denominators are the same.

π We add the numerators (the numbers at the top).

π Then, we just write our **common denominator.**

Great job! We've converted our decimal into a fraction. π

Did you notice something? π€

π The numerator is the same as the digits after the decimal point.

**0****.****2****5**** **is **25/100 or 25 hundredths.**

Here's **a quick way **to convert decimals into fractions.

**π First, **figure out the **place value of the last digit.** That will tell you what your denominator is.

The last digit in 0.25 is 5. It's in the **Hundredths **place.Β

A Hundredth is 1/100.

β So our denominator is 100.

π **Then,** find **the digits after the decimal point.** That's your numerator.

The number after the decimal point is 25.

Instead of looking at the digits separately, we just take them as part of one number.

β Our numerator is 25.

So, our answer is 25/100.

Let's use the quick way to convert decimals into fractions again.

Can you convert this?

0.4

**First, **figure out the **place value of the last digit.**

4 is the last digit. It's in the Tenths place.

A Tenth is 1/10.

β That means our denominator is 10.

**Then,** find **the number after the decimal point.**

After the decimal point, the number we see is 4.

β Our denominator is 4.

So, **0.4 **is **4/10.**

**Tip: **You can simplify 4/10 down to **2/5.**

If you don't remember how to simplify fractions, try the lesson on simplifying fractions to lowest terms.

Here's another example.

0.75

What is 0.75 as a fraction?

That's right!

**0.75 **in fraction form **is 75/100.**

**Tip:**** **You can simplify 75/100 down to **3/4!**

Now try this example:

0.03

This decimal has 0 in the Ones place and a 3 in the Hundredths place.

The digit in the Tenths place is 0, so our decimal only shows 3 Hundredths.

3 Hundredths is 3/100.

**0.03 **in fraction form is **3/100**.

Now, let's convert fractions to decimals.

Look at this example:

We can use a **place value chart **to help us.

The value of this fraction is less than 1.

So we **write 0 in the Ones place.**

After the decimal point, we **write 55 for 55 Hundredths.**

Our answer is **0.55.**

Let's try another example.

How do we convert this to a decimal?

(1) Since there are **no whole numbers **in this decimal, you **write 0 in the Ones place.** Then, **place a decimal point after it.**

(2) Check the numerator to see how many Hundredths there are.

**Write the number in the numerator **after the decimal point.

This is the **fractions part **of the decimal.

So, our answer is **0.68.**

Now let's try converting this fraction into a decimal:

There's **no whole number **so we **write 0 in the Ones place.**

Our numerator shows that there are 7 Hundredths, but no Tenths.

So, we write 0 in the Tenths place, and 7 in the Hundredths.

**7 /100 **in decimal **is 0.07.**

π Tip: When you have **a fraction with a single-digit numerator,** be careful that you write your Hundredths digit in the correct place.

Good job! Why don't you try practice? πͺ

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