Converting Between Decimals and Fractions

Objective

Know how to convert a fraction to a decimal, and how to convert a decimal to a fraction.

Example

Convert the following fraction to decimal in simplest form

Answer: 2.825

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Explanation

Decimals and fractions are actually two ways of writing the same thing. In fact, in some countries, people say decimal fractions instead of decimals. Why do we have 2 ways of writing the same thing

• Fractions are often easier to imagine just by looking at them

• Decimals are often easier to do math with

So, if you want to make your math easier to do, it's good to know how to convert fractions to decimals. On the other hand, if you want to make a number look nice, it's good to know how to convert decimals to fractions

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Fraction to Decimal

To convert a fraction to a decimal, divide the numerator by the denominator

33 ÷ 40 = 0.825

Add your whole number from your fraction and you're done.

2 + 0.825 = 2.825

Answer: 2.825

Decimal to Fraction

2.825

This is a little harder.

• Whole Number: Same as the whole Number from the decimal

• Numerator: Everything after the decimal

• Denominator: Count the number of digits after the decimal. This will be the number of 0's in your denominator (first digit is always 1)

Now we need to simplify. You may see this and think, "This is going to suck." Remember this tip to make your life simpler

• For fractions that came from decimals, the only factors worth checking are 2, 5, and 10

• If 2 or 5 is not a common factor, the fraction is already in it's simplest form

For our fraction, we can see that 5 is a common factor. Dividing numerator and denominator by 5, we get

We can reduce by 5 again.

Now neither 2 nor 5 is a common factor in this fraction, so we're done.

Answer:

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Examples

Example 1

Convert the following fraction to a decimal. Round to the nearest hundredth if necessary.

4 ÷ 6 = 0.666666667

5 + 0.666666667 = 5.6666667

Rounding to nearest hundredth...

5.67

Answer: 5.67

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Example 2

3.82

We can see that 2 is a common factor. Reducing by 2...

Now, neither 2 nor 5 is a common factor in this fraction, so we're done.

Answer:

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Practice your skills

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Ready?