# Transforming Terminating Decimals to Fractions and Vice Versa04:00 minutes

Video Transcript

## TranscriptTransforming Terminating Decimals to Fractions and Vice Versa

Jim wants to make some muffins for his friend's birthday. What this has to do with writing rationals as fractions and terminating decimals, I will show you. He is searching the internet for a good recipe. Finally, he finds some really yummy looking muffins! Many of the ingredients are written as decimals of cup measurements.

### Writing fractions as decimals

But when he looks at the measuring cup, all of the measurements are given in fractions! We can help Jim transform those fractions into decimals. Let's start with one half. Fractions are just unsolved division problems. One half is the same as saying 1 divided by 2.

To solve this by hand you must write the fraction as a long division problem.

• How many times does 2 go into 1? That's hard to say. We know that our answer is going to be a decimal that is less than 1, so let's add a decimal above the division bar and rewrite 1 as 1.0.
• Now we can ignore the decimals for a bit. Instead of thinking about how many times 2 goes into 1 we can think about how many times 2 goes into 10? 2 times 5 is 10.
• So you can write the 5 after the decimal above and subtract 10 just regular long division. 10 minus 10 is zero. The zero remainder tells us that we have finished the problem.1 divided by 2 is .5 or 0.5.

Let's try the same strategy with one fourth. One fourth is the same as 1 divided by 4 which can be rewritten as a long division problem.

• Because 4 also doesn't go into 1 you should add a decimal place and a zero after the one as well as a 0 and a decimal above the division bar. 4 goes into 10 2 times. Put the 2 after the decimal.
• Since 2 times 4 is 8 you should subtract 8 from 10 to get 2. 4 doesn't go into 2 so bring down a zero.
• 4 goes into 20 exactly 5 times. Subtract 20 from 20 to get 0 remaining so you have finished the problem! 1 divided by 4 is 0.25.

### Writing decimals as fractions

Of course you can also transform decimals into fractions. Let's try 0.75 for example. 0.75 can also be called 75 hundreths because the decimal goes out to the hundreths place.

• 75 hundreths can be written as a fraction with 75 in the numerator and 100 in the denominator because we would also call this fraction 75 hundreths.
• Now, we can simplify the fraction because both numbers are divisible by 25. 75 divided by 25 is 3 and 100 divided by 25 is 4.
• The end result is three-fourths. This tells you 0.75 is three-fourths in fraction form.

Let's look at another example. 0.125. One is in the tens place, two is in the hundreths place, and the decimal ends in the thousandths place. This decimal is called one-hundred and twenty five thousandths. This tells you to write the fraction with 125 in the numerator and 1000 in the denominator.

We can simplify the fraction by dividing the top and bottom by 125. 125 divided by 125 is 1 and 1000 divided by 125 is 8. So 0.125 is 1/8 in fraction form.

After converting the measurements, Jim makes some delicious looking muffins. Not being able to resist the smell, he tries one. Yuck! The muffin tastes disgusting! He accidentally added salt instead of sugar. Poor Jim.