M7 L42 Repeating Decimals

Math 7 Lesson 42 Repeating Decimals

When a decimal number is divided and the division ends with a 0, we call the answer a TERMINATING DECIMAL. 

For example, divide 1296 ÷ 5.

When the answer does not terminate but the same set of digits repeat over and over, we call the answer a REPEATING DECIMAL and the repeating digits are called the REPETEND.

For example, divide 1294 ÷ 6

When the decimal repeats we use a bar to show which digits repeat so we don't have to write them over and over. Notice the bar is only over the digit that repeats.

Even if there is a digit in the ones place, we can still use a bar to show the repeating digits.

Multiple Choice

Which is the correct notation for 0.1666 . . . .

• 0.16 . . .

• $0.1\overline{6}$

• 0.16

• 0.166

• $0.\overline{16}$

Multiple Choice

Which is the correct notation for 454.5454545 . . .

• 454.55

• 454.0

• 454.54

•  $4\overline{54}$  

•  $454.\overline{54}$  

Fill in the Blanks

Round to five decimal places. 

 $5.31\overline{6}$  
Write out the number to six decimal places to decide whether the last digit will round up or stay the same.

Fill in the Blanks

Round to five decimal places.  $25.\overline{405}$  

Again, write the number out to six decimal places before rounding.

Multiple Choice

Of the following, which is the smallest?

 $0.\overline{6},\ 0.6,\ 0.65$  

•  $0.\overline{6}$  

• 0.6

• 0.65

Multiple Choice

Of the following, which is the largest?

 $0.\overline{6},\ 0.6,\ 0.65$  

•  $0.\overline{6}$  

• 0.6

• 0.65

Multiple Select

Check all expressions that are equal.

• 1.5/11

• 0.136...

• 0.1363636...

• $0.1\overline{36}$

• 0.136