Question

Complete the table by converting each decimal to a fraction. Show your work. Repeating decimals. 0.2, 0.5, 0.7

Describe any patterns you noticed when converting the decimals in the table

Answer 1

Answers

Part 1 = 2/9

Part 2 =5/9

Part 3 =7/9

Step-by-step explanation

To convert the a repeating decimals this are the steps;

Part 1

Let x = 0.222222... (i)

10x = 2.222222... (ii)

Subtract equation (i) from equation(ii)

10x = 2.222222....

-x = 0.222222....

9x = 2.00000..

∴ 9x = 2

Divide by 9 both sides;

x = 2/9

Part 2

Let x = 0.5555...

10x = 5.5555...

subtract equation (i) from equation (ii).

10x = 5.5555..

- x = 0.5555..

9x = 5.0000..

∴ 9x = 5

x = 5/9

Part 3

Let x = 0.7777....

10x = 7.7777...

Subtracting equation (i) from equation (ii)

10x = 7.7777...

-x = 0.7777...

9x = 7.000..

∴ 9x = 7

x = 7/9

Pattern noted

When converting the repeating decimals to fraction only one number was repeating. This made the three decimals have the same fraction.