Question

The decimal 0.34 can be represented as
A. $\dfrac{34}{100}$
B. $\dfrac{34}{1000}$
C. $\dfrac{34}{10}$
D. None of the above.

Answer 1

Hint: To convert any decimal into fraction, we have to follow these three steps.
1. Divide the given number by 1.
2. Multiply both the numerator and denominator by 10, for every number after the decimal point.
3. Simplify the fraction.

Complete step-by-step answer:

It is given in the question that we have to represent 0.34 as a fraction. The steps to convert decimals into fractions are as follows:
Let us suppose we have to convert 0.01 into a fraction, then,
Step 1: We will divide the given number by 1, so we can write 0.01 as $\dfrac{0.01}{1}$.
Step 2: Multiplying both the numerator and the denominator by 10 for every number after the decimal point. We have two numbers of digits 0 and 1 after the decimal. So, we will multiply the numerator and denominator by 100 and we get,
$\dfrac{0.01\times 100}{1\times 100}=\dfrac{1}{100}$
Step 3: In this step we will reduce the obtained fraction to its smallest ratio, but as we have $\dfrac{1}{100}$ here, which is already the smallest fraction possible, so, 0.01 can be written as $\dfrac{1}{100}$.
Now we will convert our given number of 0.34 into a fraction according to these three steps.
Step 1: We will divide 0.34 by 1 and get,
$\dfrac{0.34}{1}$
Step 2: We will multiply the numerator and the denominator by 100, as there are two digits, 3 and 4 placed after the decimal point. So, we get,
$\begin{align}
  & \dfrac{0.34\times 100}{1\times 100} \\
 & =\dfrac{34}{100} \\
\end{align}$
Step 3: We will now reduce $\dfrac{34}{100}$ into its simplest form by dividing it by 2. Then we get,
$\dfrac{\dfrac{34}{2}}{\dfrac{100}{2}}=\dfrac{17}{50}$
So, the fraction form of 0.34 can be written as $\dfrac{17}{50}$ but we have only $\dfrac{34}{100}$ in the option, so we will consider $\dfrac{34}{100}$ as the correct answer.
Therefore, option A is the correct answer.

Note: Both $\dfrac{17}{50}$ and $\dfrac{34}{100}$ are the correct answers, but as only $\dfrac{34}{100}$ is given in the options, we are considering that as the correct answer here. If it were there in the options, then multiple correct answers would have been there. So, we must observe the options also carefully.