# Question 7ae58

Sep 10, 2017

Form a fraction as:

" whole number" ("all decimals - non-recurring")/(color(red)(9)" for do recur and "color(blue)(0) " for don't recur")

#### Explanation:

In all of these recurring decimals, not all of the decimals recur.

While there is a full method to determine the fractions, here is the short cut rule which can be applied.

From the example given, note the following:

$1 \textcolor{b l u e}{.4} \overline{\textcolor{red}{2}} = 1 \textcolor{b l u e}{.4} \textcolor{red}{2222222. \ldots} \leftarrow 2 \text{ recurs", color(blue)(4) " does not}$
(the whole number is $1$)

$= 1 \frac{42 - 4}{90} = \frac{38}{90} = \frac{19}{45}$

Form a fraction as:" whole number" ("all decimals - non-recurring")/(color(red)(9)" for do and "color(blue)(0) " for don't")#

$0.2 \overline{7} = \frac{27 - 2}{90} = \frac{25}{90} = \frac{5}{18}$

$4.6 \overline{5} = 4 \frac{65 - 6}{90} = 4 \frac{59}{90}$

$8.23 \overline{7} = 8 \frac{237 - 23}{900} = \frac{214}{900} = 8 \frac{107}{450}$

$816.14 \overline{35} = 816 \frac{1435 - 14}{9900} = 816 \frac{1421}{9900}$

$200 79 \overline{125} = 200 \frac{79125 - 79}{99900} = 200 \frac{79046}{99900} = 200 \frac{39523}{49950}$