Rational Numbers and Decimals

Rational Numbers and Decimals

​In the chat, type what you already know about fractions and decimals.

Describing Decimal Forms of Rational Numbers

A rational number  is a number that can be written as a ratio of two integers a and b, where b is not zero.
In other words, numbers that can be written as fractions.

For example,  $\frac{4}{7}$   is a rational number, as is 0.37 because it can be written as the fraction  $\frac{37}{100}$  

Open Ended

Use a calculator to find the equivalent decimal form of each fraction. Remember that numbers that repeat can be written as 0.3333... or 

 $0.\overline{33}$  

 $\frac{1}{4}=$  
 $\frac{5}{8}=$  
 $\frac{2}{3}=$  
 $\frac{2}{9}=$  
 $\frac{12}{5}=$  

Open Ended

Now find the corresponding fraction of the decimal equivalents given.

0.2 =

0.875 =

Open Ended

Do you think a negative sign affects whether or not a number is a rational number? Use as  $-\frac{1}{2}$   an example.

Writing Rational Numbers as Decimals

You can convert a rational number to a decimal using long division.

Some decimals are terminating decimals because the decimals come to an end.

Other decimals are repeating decimals because one or more digits repeat forever. 

Write  $\frac{5}{16}$   as a decimal. 

• The numerator goes inside the house

• Since 16 does not go into 5, we add ".0" after the 5

• Begin division

• Add zeros when neccessary

Write  $\frac{13}{33}$   as a decimal. 

• The numerator goes inside the house

• 33 goes into 13 zero times

• No more digits left, so we add ".0"

• Add zeros when neccessary

Fill in the Blank

Write each rational number as a decimal using long division.

 $\frac{1}{3}=$  

Fill in the Blank

 $\frac{9}{20}=$  

Write $6\ \frac{3}{4}$  as a decimal.

Fill in the Blank

 $2\ \frac{3}{4}=$  

Multiple Choice

Is the decimal equivalent terminating or repeating decimal?

• Terminating

• Repeating

Fill in the Blank

 $7\ \frac{1}{3}=$  

Multiple Choice

Is the decimal equivalent terminating or repeating decimal?

• Terminating

• Repeating