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

Answers

Part 1 = 2/9

Part 2 = 5/9

Part 3 = 7/9

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.