Lesson 2 MGSE8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. I can… …convert repeating decimals into a fraction.

Repeating Decimals All repeating decimals can be written as fractions They are ‘rational numbers’

Recurring Decimals  

Changing a repeating decimal with 1 number repeating

Changing a repeating decimal with multiple numbers repeating

Is there another method? YES! Method 2 Click on link

Repeating Decimals e.g. 0.333333333… Let x = 0.333333333… Then 10x = 3.333333… We do a subtraction…

10x = 3.33333333… - x = 0.33333333… 9x = 3 X = 3 = 1 9 3

e.g. 0.565656… Let x = 0.5656565… 100x = 56.56565656… We do a subtraction…

100x = 56.56565656… - x = 0.565656565 99x = 56 X = 56 99

Now you try Convert the decimals to fractions 0.545454….. 0.599999….