Question

3.123 (bar on 23 ) convert into p q form

Answer 1

Answer:

a) 1546/495

Step-by-step explanation:

3.123 bar

x = 3.123 bar

10x = 31.23 bar ------- Equation 1

1000x = 3123.23 bar ------- Equation 2

Substract 1 from 2

1000x - 10x = 3123.23 bar - 31.23 bar

990x = 3092

x = 3092/990

x = 1546/495 ( on simplifying )

Answer 2

$\displaystyle \bf{ 3. 1\overline{23} = \frac{1546}{495} }$

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

Given :

The number $\displaystyle \sf{ 3. 1\overline{23} }$

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 $\displaystyle \sf{ 3. 1\overline{23} }$

Step 2 of 2 :

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

$\displaystyle \sf{ Let \: \: x = 3. 1\overline{23} }$

Then x = 3.123232323... - - - - - - - (1)

Multiplying both sides by 10 we get

10x = 31.23232323... - - - - - - (2)

Multiplying both sides of Equation 1 by 1000 we get

1000x = 3123.23232323... - - - - - - (3)

Equation 3 - Equation 2 gives

990x = 3092

$\displaystyle \sf{ \implies x = \frac{3092}{990} }$

$\displaystyle \sf{ \implies x = \frac{1546}{495} }$

$\displaystyle \sf{ \therefore \: \: 3. 1\overline{23} = \frac{1546}{495}}$

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

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