FRACTIONS TO DECIMALS

What Are Fractions?

A fraction is really a division statement. The number ½ says that we divided 1 whole thing into 2 equal parts. Similarly, ¾ indicates that we divided something -- say a pizza -- into 4 equal parts and we ate 3 of them. It could also mean that we have 4 things of equal size or value and 3 of them are of interest because of some quality, say they're red or they've been eaten. So if we ordered 4 pizzas and ate 3 of them, we'd have eaten ¾ of all the pizzas.

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Changing Fractions to Decimal Equivalents by Division

Here's some fraction images

Since a fraction indicates division, that's exactly how we change it into a decimal. We do the division. So, to get the decimal equivalent of ¾, we divide 4 into 3 like this:

However, if we're smart, we'll just remember that three "quarters" = 75 cents so ¾ = 0.75.

To find the decimal equivalent of a fraction,
divide the numerator by the denominator.

Repeating Decimals

When we use division to find the decimal equivalent of fractions with 3, 7, 9, 11 etc.in the denominator, the quotient is a repeating digit. These are called repeating decimals and as always in math, we use a precise symbol to denote them.

Let's use division to find the decimal equivalent of .

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We must make sure the "bar" is over ALL THE REPEATING DIGITS in the pattern!

For instance, .
and
Note that the bar covers all 6 repeating digits.

The decimal equivalent of 1/19 = 0.052631578947368421 052631578947368, with 18 repeating digits in the pattern. All 18 must be covered by the bar.

Changing the Denominator to a Power of 10

Since the denominator of any decimal's fraction equivalent is a power of 10, when we have to find a fraction equivalent to a decimal value, and it's easy to make the denominator a power of 10 through multiplication by a fraction equal to 1, we can proceed like this.

We know that 5 × 20 = 100 so we multiplied by 5/5 which equals 1 -- therefore we didn't change the value of our fraction -- we just wrote an equivalent fraction with a denominator of 100.
In the second case, we knew that 8 × 125 = 1000, so we multiplied by 8/8.

When we have mixed numbers -- part whole number, part fraction, we change the fraction part to its decimal equivalent and write the whole number as usual. So 1¼ = 1.25

Now get a pencil, an eraser and a note book, copy the questions,
do the practice exercise(s), then check your work with the solutions.
If you get stuck, review the examples in the lesson, then try again.

Practice

1) Multiply by 1 to make the denominator a power of 10, then write the decimal equivalent.

a) b) c) d) e)

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2) Find the decimal equivalent by division. Round to 3 decimal places. Indicate repeats.

a) b) c) d) e)

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3) Write the fraction equivalent of these decimals. Reduce to lowest terms.

a) 0.36 = b) 0.012 = c) 0.6 = d) 0.237 = e) 0.0027 =

Solutions

1) Change each denominator to a power of 10, then write the decimal equivalent.

a) b) c)
     
d) e)  

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2) Use division to find the decimal equivalent of these fractions. Round to 3 decimal places.

a) 0.267

b) 0.417

c) 0.714

d) 0.727

e) 0.444

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3) Write the fraction equivalent of these decimals. Reduce to lowest terms.

a) 0.36 = b) 0.012 = c) 0.6 =
     
d) 0.237 = e) 0.0027 =  

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