Can someone show me how to convert a repeating decimal into a rational number? studying for a test : /

Move the decimal point to the right the number of places equal to the number of repeating digits. Subtract the original number. (Digits after the first instance of the pattern will be canceled.) Divide the result by a number of 9s equal to the number of repeating digits. Simplify the result.

Example: 5.3181818_18

There are 2 repeating digits, so we subtract ...

... 531.8_18 -5.3_18 = 526.5

and divide by 99 . . . . . . two 9s, one for each of the two repeating digits

... = 526.5/99 = 5625/990 = 117/22 = 5 17/22

More formally, if S is the value of the original number, and it has n repeating digits, you compute

.. (S·10^n - S)/(10^n -1) = S(10^n -1)/(10^n -1) = S

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°