Answer:
[tex]\text{0.1414... in fraction is }\frac{14}{99}[/tex]
Step-by-step explanation:
Given the number 0.1414...
we have to represent the above in terms of fraction
Let x=0.1414.... → (1)
Multiplying by 100 on both sides
100x=14.1414.... → (2)
Subtract (1) from (2), we get
[tex]99x=14[/tex]
[tex]x=\frac{14}{99}[/tex]
[tex]\text{Hence, 0.1414... in fraction is }\frac{14}{99}[/tex]
A repeating number is a number where some given number of digits repeats infinitely.
We will find that the fraction is 14/99
Here we start with:
x = 0.141414...
The first thing we need to do is find the number of repeating decimals.
Here we have 1 and 4 (two repeating decimals)
Then we need to multiply our number by 10^2 (the exponent is the same as the number of repeating digits).
We will get:
x*10^2 = x*100 = 0.141414...*100 = 14.1414...
Now we can subtract the original number:
x*100 - x = 14.1414... - 0.1414... = 14
x*99 = 14
Now we can solve this for x:
x = 14/99
Then we got:
0.1414... = 14/99
We just wrote our number as a fraction.
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