Question

How do you convert $2.48$ into a percentage and fraction?

Answer 1

Hint: To solve this problem we should know about fraction and percentage:
Fraction: It represents an equal part of a whole or a collection.
Percentage: it is a number or ratio expressed as a fraction of $100$ . It is a dimensionless number.

Complete step by step solution:
Given number is $2.48$
We have to convert it into percentage and fraction.
So to convert into percentage:
We will simply multiply the given number with $100$ and add $\% $ symbol after it.
So, $2.48 \times 100 = 248\% $
To convert it into fraction;
We will go step by step:
Step 1: write down the number as a fraction of one;
 $2.48 = \dfrac{{2.48}}{1}$
Step 2: Multiply both top and bottom by $10$ for every number after the decimal points;
So, we will here multiply $100$ as two numbers after the decimal.
 $\dfrac{{2.48}}{1} = \dfrac{{2.48 \times 100}}{{1 \times 100}} = \dfrac{{248}}{{100}}$
Step 3: simplify or reduce the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD $(248,100) = 4$ .
So,
 $\dfrac{{248 \div 4}}{{100 \div 4}} = \dfrac{{62}}{{25}}$
As the numerator is greater than the denominator, we have an improper fraction, so we convert it into mixed number, thus
Step 3: divide $62$ by $25$ and the dividend is $2$ and reminder is $12$
 $\dfrac{{248}}{{100}} = 2\dfrac{{12}}{{25}}$

Hence, we can write $2.48$ in fractional form as $2\dfrac{{12}}{{25}}$ and in percentage from as $248\% $.

Note: Type of fraction:
- Unit fraction: the numerator is $1$ is called a unit fraction.
- Proper fraction: if numerator value is less than the denominator value.
- Improper fraction: if numerator value is more than the denominator value.
- Mixed fraction: if the fraction consists of the whole number with a proper fraction.