Decoding Terminating Decimals and Repeating Decimals through Long Division and Rational Numbers

Fraction	Decimal
$\frac{2}{9}$
$\frac{1}{3}$
$\frac{3}{4}$
$\frac{4}{1 1}$
$\frac{3}{8}$

Fraction

Decimal

\frac{2}{9}

\frac{1}{3}

\frac{3}{4}

\frac{4}{1 1}

\frac{3}{8}

Repeating Decimal Numbers
Number	Notation	Fraction
$0.666666 \dots$	$0 . \overline{6}$	$\frac{2}{3}$
$1.533333 \dots$	$1.5 \overline{3}$	$\frac{2 3}{1 5}$
$5.373737 \dots$	$5 . \overline{37}$	$\frac{5 3 2}{9 9}$

Repeating Decimal Numbers

Number

Notation

Fraction

0.666666 \dots

0 . \overline{6}

\frac{2}{3}

1.533333 \dots

1.5 \overline{3}

\frac{2 3}{1 5}

5.373737 \dots

5 . \overline{37}

\frac{5 3 2}{9 9}

Terminating Decimal Numbers
Number	Fraction
$0.5$	$\frac{1}{2}$
$1.53$	$\frac{1 5 3}{1 0 0}$
$52.372$	$\frac{1 3 0 9 3}{2 5 0}$

Terminating Decimal Numbers

Number

Fraction

0.5

\frac{1}{2}

1.53

\frac{1 5 3}{1 0 0}

52.372

\frac{1 3 0 9 3}{2 5 0}

Genre

Number of Students

Action

6

Animation

12

Comedy

4

Science Fiction

5

a Start by finding the total number of students in the class.

Genre	Number of Students
Action	$6$
Animation	$12$
Comedy	$4$
Science Fiction	$5$
Total	$27$

There are

27

students in the class. Of those students,

12

prefer animation. This can be represented by a fraction by writing the part, the

12

students who like animation, over the whole, the

27

students in the class.

\frac{1 2}{2 7}

Since the given options are decimals, this fraction must be converted into a decimal number. To do so, use long division. Don't stop until the remainder is

0

or a pattern appears.

It appears that the remainder will always repeat — in other words, the digit

4

in the quotient will always repeat. This means that the division resulted in a repeating decimal number.

\frac{1 2}{2 7} = 0.444 \dots

The same value can also be written by drawing a bar over the repeating digit.

\frac{1 2}{2 7} = 0 . \overline{4}

The answer is A.

b From the table, it can be seen that

4

students like the comedy genre. This means that the fraction of those students is

\frac{4}{2 7} .

Again, use long division to rewrite it as a decimal. Don't stop until the remainder is

0

or a pattern appears.

In this case, more than one digit repeats in the quotient.

\frac{4}{2 7} = 0.148148 \dots

Put a bar above those three digits. This repeating decimal corresponds to option C.

\frac{4}{2 7} = 0 . \overline{148}

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Catch-Up and Review

Decimal Forms of Fractions

Extra

Repeating Decimals

Terminating Decimals

Identifying Types of Decimals

Converting a Fraction Into a Repeating Decimal Number

Favorite Movie Genres

Hint

Solution

Converting a Repeating Decimal Number Into a Fraction

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