Question

How does one express the decimal $0.34$ as a fraction in its simplest form?

Answer 1

Hint: For solving this particular question , we first consider $x = 0.34$ as our first equation then multiply both the side of the first equation by hundred and then consider the resulting equation as our second equation. Lastly, we have to reduce it in its simplest form, then you will get then desired result.

Complete step-by-step solution:
We have given the decimal number $0.34$ .
Now, let us consider $x = 0.34.......................(1)$ ,
Now multiply the equation one by $100$. We will get the following,
$
   \Rightarrow x \times 100 = 0.34 \times 100 \\
   \Rightarrow 100x = 34 \\
 $
Now consider $100x = 34................(2)$
Now we divide equation second by hundred,
$ \Rightarrow x = \dfrac{{34}}{{100}}$
$
   \Rightarrow x = \dfrac{{2 \times 17}}{{2 \times 50}} \\
   \Rightarrow x = \dfrac{{17}}{{50}} \\
 $

Hence, we have the required decimal $0.34$ as a fraction in its simplest form.

Additional Information: Prime factorization is a way to write a composite number as the product of prime factors. Prime factors are those numbers or factors which are greater than one and have exactly two factors one is the number itself and other is one . There are basically two ways to find prime factorization namely ,
a) by division method
b) by factor tree

Note: While simplifying the fraction you have to write the number into its simplest form that is to express the number in its prime factors, Prime factorization: It’s the process where the original given number is expressed as the product of prime numbers. Then we have to find the same prime numbers present in the denominator as well as the numerator , then we have to cancel those common prime factors.