Question

6. The simplest form of the rational number 0. 196 is
a) 1/6
b) 3/6
c)13/66
d) 2/5​

Answer 1

Answer:

196/1000=98/500=49/250

Explanation:

I hope it's help you

Answer 2

$\displaystyle \bf 0. 1\overline{96} = \frac{13}{66}$

Which is the required simplest form of the rational number [ The correct option is c) 13/66 ]

Correct question : The simplest form of the rational number $\displaystyle \sf{ 0. 1\overline{96} }$ is

a) 1/6

b) 3/6

c) 13/66

d) 2/5

Given :

The number $\displaystyle \sf{ 0. 1\overline{96} }$

To find :

The simplest form of the rational number $\displaystyle \sf{ 0. 1\overline{96} }$ is

a) 1/6

b) 3/6

c) 13/66

d) 2/5

Solution :

Step 1 of 2 :

Write down the given number

The given number is $\displaystyle \sf{ 0. 1\overline{96} }$

Step 2 of 2 :

Find the simplest form of the rational number

$\displaystyle \sf{ Let \: \: x = 0. 1\overline{96} }$

Then x = 0.196969696..... - - - - - - - (1)

Multiplying both sides by 10 we get

10x = 1.96969696..... - - - - - - (2)

Again multiplying both sides by 100 we get

1000x = 196.96969696..... - - - - - - (3)

Equation 3 - Equation 2 gives

990x = 195

$\displaystyle \sf{ \implies x = \frac{195}{990} }$

$\displaystyle \sf{ \implies x = \frac{13}{66} }$

$\displaystyle \sf{ \therefore \: \: 0. 1\overline{96} = \frac{13}{66}}$

Which is the required simplest form of the rational number

Hence the correct option is c) 13/66

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