 Use long division to convert negative fractions to decimal numbers

Lesson

In Dashes to Dots we learnt how to convert fractions to decimals. We learnt that if a fraction has a denominator of $10$10, $100$100, $1000$1000 or any other multiple of ten, we can write it as a decimal using our knowledge of the place value table. If not, it may be helpful to use division.

No we are going to look at how to do this process using long division.

What happens if our fraction contains one or even two negative numbers?

Well, since a fraction can be written as a division question, the same rules apply as when we're dividing with negative numbers.

Remember!

The important things to remember are:

• The quotient of two negative numbers is a positive answer.
• The quotient of one positive and one negative number is a negative answer.

Examples

Question 1

Some rational numbers and their decimal equivalents are included in the given table.

When rational numbers are written as a decimal, they can be which two kinds of decimals?

 $\frac{1}{2}$12​ $\frac{1}{3}$13​ $\frac{1}{4}$14​ $\frac{1}{5}$15​ $\frac{1}{6}$16​ $\frac{1}{7}$17​ $\frac{1}{8}$18​ $\frac{1}{9}$19​ 1/10 1/11 $0.5$0.5 $0.3333$0.3333... $0.25$0.25 $0.2$0.2 $0.1666$0.1666... $0.142857142857$0.142857142857... $0.125$0.125 $0.1111$0.1111... 0.1 0.090909...

A) Terminating decimals     B) Non-terminating decimal with repeated pattern     C) Non-terminating decimal with no repeated pattern

Think: Which of these options described those given in the table above. Note a terminating decimal is one that doesn't go on forever.

Do: In this table there are:

A) terminating decimals (e.g. $0.5$0.5, $0.25$0.25) , and

B) non-terminating decimal with repeated pattern  (e.g. $0.3333$0.3333..., $0.1666$0.1666...)

Question 2

Use the long division algorithm to convert $\frac{-7}{10}$710 to a decimal.

a) First, use long division to convert $\frac{7}{10}$710 to a decimal.

b) Hence, write $\frac{-7}{10}$710 as a decimal.

Question 3

The first two decimal place values in converting  $\frac{1}{15}$115 to a decimal are given.

a) Continue the long division process to find the next two decimal place values.

b) When $\frac{1}{15}$115 is expressed as a decimal, which of the following is the repeated pattern after the decimal point?

A) 060 606 060...

B) 066 666 666...

C) 066 066 066...

c) Hence convert $\frac{-1}{30}$130 to a decimal, giving your answer to three repeated terms.