# Come si converte 0.916 (6 ripetizioni) in una frazione?

#### Risposta:

0.91bar(6) = 11/12

#### Spiegazione:

In case you have not encountered it, you can indicate a repeating sequence of digits in a decimal expansion by placing a bar over it.

Così:

0.91666... = 0.91bar(6)

color(white)()
Metodo 1

Moltiplicato per 100(10-1) = 1000-100 per ottenere un numero intero:

(1000-100) 0.91bar(6) = 916.bar(6) - 91.bar(6) = 825

Dividi entrambe le estremità per 1000-100 trovare:

0.91bar(6) = 825/(1000-100) = 825/900 = (color(red)(cancel(color(black)(75)))*11)/(color(red)(cancel(color(black)(75)))*12) = 11/12

Perché 100(10-1) ?

The factor 100 shifts the given number two places left, leaving the repeating section starting just after the decimal point. The factor (10-1) shifts the number a further 1 place - the length of the repeating pattern - then subtracts the original to cancel out the repeating tail.

color(white)()
Metodo 2

Dato:

0.91bar(6)

Recognise the repeating 6 tail as the result of dividing by 3, so multiply by color(blue)(3) trovare:

color(blue)(3) * 0.91bar(6) = 2.75

Notare che 2.75 ends with a 5, so we can attempt to simplify the decimal by multiplying by color(blue)(2):

color(blue)(2) * 2.75 = 5.5

Notare che 5.5 ends with a 5, so we can attempt to simplify by multiplying by color(blue)(2) ancora una volta:

color(blue)(2) * 5.5 = 11

Having arrived at an integer, we can divide by the numbers we multiplied by to get a fraction:

0.91bar(6) = 11/(2*2*3) = 11/12