Converting 84% to Its Equivalent Decimal and Fraction Forms

Video Solution

Solution Steps

00:00 Convert from percentages to fractions

00:05 The percentage equals a fraction where the numerator is the percentage (X) and the denominator is 100

00:10 Apply this formula to our exercise

00:25 We'll factor 84 into 21 and 4, and 100 into 25 and 4

00:30 Reduce wherever possible

00:33 This is the solution

Step-by-Step Solution

To solve this problem effectively, follow these steps:

Step 1: Convert the percentage to a fraction.
To express 84% as a fraction, write it as $\frac{84}{100}$ since percent means per hundred.
Step 2: Simplify the fraction.
We need to simplify $\frac{84}{100}$ by finding the greatest common divisor (GCD) of 84 and 100. The GCD of 84 and 100 is 4.
Step 3: Divide both numerator and denominator by their GCD.
Divide 84 by 4 to get 21, and divide 100 by 4 to get 25.
Thus, $\frac{84}{100} = \frac{21}{25}$ .
Step 4: Identify the correct choice.
Among the provided options, $\frac{21}{25}$ corresponds to choice 2.

Thus, the percentage 84% is equal to $\frac{21}{25}$ .