Question

What id the decimal number in fraction of 0.3434?

Answer 1

Given :   0.3434

To Find : Fraction

Solution:

0.3434

= 3434/10000

= 1717/5000

0.3434 = 1717/5000

if Question is 0.3434...

N = 0.3434...

100N = 34.3434...

=> 99N = 34

=> N = 34/99

0.3434... = 34/99

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Answer 2

Note The decimal number is $\[0.34\overline {34} \]$

Given,

Decimal number $\[ = 0.34\overline {34} \]$

It is a recurring number.

Solution,

Consider,

$\[x = 0.34\overline {34} \]$-----------(1)

Multiply by 100 on both side,

$\[\begin{array}{l}100x = 100 \times 0.34\overline {34} \\ \Rightarrow 100x = 34.34\overline {34} \end{array}\]$------------(2)

Subtract equation 1 from equation 2,

$\[\begin{array}{l}100x - x = 34.34\overline {34} - 0.34\overline {34} \\ \Rightarrow 99x = 34\\ \Rightarrow x = \frac{{34}}{{99}}\end{array}\]$

Hence the fraction form of this number is $\[\frac{{34}}{{99}}\]$.