Question

0.32 (bar on 2) express in form of p/q

Answer 1

$\displaystyle \bf{ 0.3 \overline{2} = \frac{29}{90} }$

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

Given :

The number $\displaystyle \sf{ 0.3 \overline{2} }$

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 $\displaystyle \sf{ 0. 3\overline{2} }$

Step 2 of 2 :

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

$\displaystyle \sf{ Let \: \: x = 0. 3\overline{2} }$

Then x = 0.322222... - - - - - - - (1)

Multiplying both sides by 10 we get

10x = 3.22222... - - - - - - (2)

Multiplying both sides of Equation 1 by 100 we get

100x = 32.22222... - - - - - - (3)

Equation 3 - Equation 2 gives

90x = 29

$\displaystyle \sf{ \implies x = \frac{29}{90} }$

$\displaystyle \sf{ \therefore \: \: 0. 3\overline{2} = \frac{29}{90}}$

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

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$1.$ The sum of 0.3 bar and 0.2 bar is

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Answer 2

Answer:

29 / 90

Step-by-step explanation:

Let x = 0.3222......

  10x = 3.2222....... (i)

100x = 32.2222..... (ii)

Now, subtracting (i) from (ii) :

100x - 10x = (32.222....) - (3.2222....)

      90x    =  29

           x    = 29 /90

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