Question

convert into p/q form 12.625(625 recurring)​

Answer 1

Answer:

Hint: In order to find a solution to this problem, we shall denote the recurring decimal by a variable. Then, we will multiply by 10 on both sides to get only the recurring digits after the decimal point. Then, finally we will subtract the resulting equations to get the required fraction i.e. in p/q form.

Step-by-step explanation:

Hint: In order to find a solution to this problem, we shall denote the recurring decimal by a variable. Then, we will multiply by 10 on both sides to get only the recurring digits after the decimal point. Then, finally we will subtract the resulting equations to get the required fraction i.e. in p/q form.

Answer 2

$\displaystyle \bf{ 12.625(625 recurring) = \frac{12613}{999} }$

Which is of the form p/q where p , q are integers and q ≠ 0

Given :

The number $\displaystyle \sf{ 12.625(625 recurring) }$

To find :

To express in the form p/q where p , q are integers and q ≠ 0

Solution :

Step 1 of 2 :

Write down the given number

The given number is $\displaystyle \sf{12.625(625 recurring) }$

Step 2 of 2 :

Express in the form p/q where p , q are integers and q ≠ 0

$\displaystyle \sf{ Let \: \: x = 12.625(625 recurring) }$

$\displaystyle \sf{ \implies }x = 12. \overline{625}$

⇒ x = 12.625625625... - - - - - - - (1)

Multiplying both sides by 1000 we get

1000x = 12625.625625625... - - - - - - (2)

Equation 2 - Equation 1 gives

999x = 12613

$\displaystyle \sf{ \implies x = \frac{12613}{999} }$

$\displaystyle \sf{ \implies x = \frac{12613}{999} }$

$\displaystyle \sf{ \therefore \: \: 12.625(625 recurring) = \frac{12613}{999}}$

Which is of the form p/q where p , q are integers and q ≠ 0

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