Fractions and Decimals

A rational number is a number that can be written as a quotient ,  where a and b are integers and b ≠ 0.

The diagram shows how rational numbers, integers, and whole numbers are related.

To write any rational number   as a decimal, divide a by b. If the quotient has a remainder of zero, the result is a terminating decimal. If the quotient has a digit or group of digits that repeats without end, the result is a repeating decimal.

Writing Fractions as Decimals

To write a fraction as a decimal, divide the numerator by the denominator.

Example 1
The quotient 0.4545. . . is a repeating decimal.

To indicate this, place a bar over the repeating digits:

Example 2

The remainder is zero, so   = 0.35, a terminating decimal.

Ordering Rational Numbers

The table lists the lengths of five finches. Order the finches from shortest to longest.

Step 1)  Write mixed numbers as decimals.

Step 2)  Graph all the finches' lengths on a number line.

Answer:  From shortest to longest they are--

painted bunting, lazuli bunting, indigo bunting, house finch, purple finch.

Guided Practice  (Ask your tutor for help.)

Order the numbers from least to greatest.

To write a terminating decimal as a fraction or mixed number, use the place value of the decimal's last digit to determine the denominator. For example, you can write 0.37 as 37/100 or thirty-seven hundredths because 7 is in the hundredths' place.

Writing Terminating Decimals as Fractions

Write the decimal as a fraction or mixed number.

Example 1 

Example 2

Repeating Decimals

To write a repeating decimal as a fraction or mixed number, form two equivalent equations by multiplying by a power of 10 then subtract the equations.

Writing Repeating Decimals as Fractions

Example

Step 1

Step 2

Step 3
Solve for x.  Simplify.

Guided Practice  (Ask your tutor for help.)

Write the decimal as a fraction or mixed number.

Tell whether the number is included in each of the following number groups: rational number, integer, whole number.

    0

   0.55

    -14

Which list is in order from least to greatest?

In a class, 22/25 of the students are right-handed.  What is another way to express this number?

A.   0.22
B.   0.25
C.   0.47
D.   0.88

Use the table below. It tells the fraction of students in a survey that named each breakfast food as their favorite.

Write each fraction as a decimal and order the foods from most popular to least popular.

How many more students picked the most popular food than the least popular food  if 1200 students responded to the survey?

The total area of the United States is about 3,718,000 square miles. The portion of this area that is covered by water is . 

Express this fraction as a decimal rounded to three places.