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Math for Kids23 chapters | 325 lessons

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Lesson Transcript

In this lesson, you'll learn how fractions and decimals represent parts of a whole. You'll also learn how to convert fractions into decimals and practice with a few examples.

Detective Sahmaj is on a quest to find some stolen treasure. His clue is a combination to a locked room inside an abandoned warehouse. Detective Sahmaj reaches the door and gets ready to enter the combination into the lock, but to his surprise, the lock can only be opened using numbers in decimal form. But the detective's clue is made of fractions! How will he solve this mystery?

Fractions and decimals are both ways to represent parts of a whole - both a fraction and a decimal express a number that is less than one. Detective Sahmaj needs to convert his fractions into decimals. Sometimes, in order to complete a math problem, you will also need to convert a fraction into a decimal. Let's look at the process and solve Detective Sahmaj's mystery.

When you read a **decimal number**, which is a way of expressing a number less than one with the use of a period, it's easy to see the relationship between decimals and fractions. The decimal number 0.5 is read 'five-tenths.' That is the same way you would read this fraction: 5/10. Really, the only thing that makes a **fraction** different from a decimal is that it expresses a number less than one with a dash or a slash symbol. So really, a decimal can be written as a fraction using its place value. Look at these examples:

As you can see, we have our 0.5 to 5/10 example, but we also have 0.05 equaling five one-hundredths and 0.005 equaling five one-thousandths. It just goes up from there based on the number of zeros. It's really as simple as that. But, how do we get these decimals to turn into fractions?

Now that we understand the meaning of decimals, it's time to change fractions into decimals. The line in a fraction that separates the numerator from the denominator means ''divided by.'' The fraction 2/5 can be read as two-fifths, or it can be read as two divided by five. To turn a fraction into a decimal, we divide the numerator by the denominator.

Let's convert Detective Sahmaj's first fraction, 2/5, into a decimal. We will review the steps of long division while we solve this problem:

Let's look at this division problem. The numbers are colored to help you follow the explanation:

- Purple step: 2 divided by 5 means the 2 is placed inside the division house and the 5 is outside.

- Blue step: 5 doesn't go into 2, so we place a 0 in the answer (quotient) spot. We multiply 5 by 0 and get 0. Subtract that from 2, and we get 2.

- Green step: Add a decimal and a 0 after the 2, since we know that we can add zeroes after the decimal point without changing the value of the 2.

- Orange step: We bring down the zero. We make sure that the decimal we added to the 2.0 is also added to the quotient, so that any further numbers in the quotient will fall after the decimal point. Now, we divide 20 by 5. The answer is 4, which we place after the decimal in the quotient spot. Multiply 5 by 4 and get 20. Subtract it from the 20, and the answer is 0. The problem is finished.

- The answer is 0.4. When the fraction 2/5 is turned into decimal, it is 0.4.

Now, we're ready to solve the combination Detective Sahmaj was looking at.

Let's start with 2/5:

- The first number in Detective Sahmaj's combination was 2/5, which equals 0.4

Now, let's look at 3/4:

- 3/4 is 3 divided by 4, which equals 0.75

Now, let's take a look at 1/2:

- 1/2 is 1 divided by 2, which equals 0.5, which you might remember from earlier in the lesson

What about 9/10?

- Well, 9/10 is 9 divided by 10, which is 0.9

Now that Detective Sahmaj has solved the combination, he can use it to enter the locked room and find the stolen treasure!

Okay, let's take a brief moment to review what we've learned.

Fractions and decimals are both ways to represent parts of a whole. Really, the only thing that separates the two is the fact that a **decimal** is a way of expressing number less than one with the use of a period, while a **fraction** expresses a number less than one with a dash or a slash symbol. To convert a fraction into a decimal, it's really as simple as dividing the numerator by the denominator. Now, you should be just as good as Detective Sahmaj at cracking that combination lock.

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Additional Activities

**1.** Convert the decimal 0.25 into a reduced fraction form.

**2.** Using division, convert the fraction 7/8 into a decimal.

**1.** The decimal, 0.25, has two decimal places. Hence, its fraction form will be obtained by taking the decimal without the decimal point and dividing it by the second power of 10. Thus, we get 0.25 = 25/10^2 = 25/100.

Now, we can reduce the fraction 25/100 by dividing the numerator and denominator both by 5 to get 25/100 = 5/20. Then, we divide the numerator and denominator both by 5 again to obtain 5/20 = 1/4.

**Hence, the fraction form of 0.25 is 1/4.**

**2.** To convert the fraction into a decimal form, we note the fraction form denotes 7/8, or 7 divided by 8. This gives us the following division:

Step 1: 8 goes into 7 zero times, leaving us with remainder **7**. The quotient at this step is **0** with a decimal point in front of it.

Step 2: Bringing down a 0, then 8 goes into 70 eight times, leaving a remainder **6**. The quotient gets added a digit **8** following the decimal point in the step above.

Step 3: Bringing down a 0 again, then 8 goes into 60 seven times, leaving a remainder **4**. The digit **7** is appended to the quotient in the step above.

Step 4: Bring down a 0. Then 8 goes into 40 five times, leaving a remainder of **zero**. The digit **5** gets added to the quotient above.

**Hence, the final answer is 0. 875**.

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Math for Kids23 chapters | 325 lessons

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