Question

How do you convert 0.916 (6 repeating) to a fraction?

Answer 1

11/12

Explanation:

1. Let x = 0.916 (6 repeating)

2. Identify the FIRST repeating digit's place value:

6 is in the 1000ths place

3. Multiply BOTH sides of x = ... by the value you got in step 2

x = 0.916 (6 repeating)

1000x = 916.6 (6 repeating)

4. Subtract the x = ... from the 1000x = ...:

1000x = 916.666...

x = 0.916...

999x = 915.75

5. Divide both sides by 999:
`x=(915.75)/(999)`

6. Rewrite as a corrected fraction:
`x=(91575)/(99900)`

7. Simplify as far as possible:
`x=(91575)/(99900)/(8325)/(8325)=(11)/(12)`

Answer 2

Explanation:

0.91666666...

is the sum of

0.91 and 0.006666666...

0.66666666... = 2/3

0.0066666666... = 2/300

0.91 = 91/100

so,

0.91666666... = 91/100 + 2/300 =

= 91×3/300 + 2/300 =

= 273/300 + 2/300 = 275/300 =

= 11/12

if you fail to find a fraction at the beginning (like the 2/3 we did), remember the following basics

0.1111111111... = 1/9

0.2222222... = 2/9

0.33333333... = 3/9 = 1/3

0.44444444... = 4/9

0.55555555... = 5/9

0.66666666... = 6/9 = 2/3

0.777777777... = 7/9

0.88888888... = 8/9

0.99999999... = 9/9 = 1

if you want to repeat a pattern like

0.125 to

0.125125125125125...

remember this simple trick

0.125 = 125/1000

0.125125125125125... = 125/999

you must use as many 9s as you have digits in the basic pattern.

227/999 = 0.227227227227227...

6382/9999 = 0.63826382638263826382...

and so on.