How do you write 1/2 as a percentage?
The correct answer and explanation is:
The fraction 1/2 written as a percentage is 50%.
Here’s a detailed explanation of how to convert 1/2 into a percentage:
A percentage is a way of expressing a fraction or a ratio as a part of 100. The word “percent” literally means “per hundred” or “out of one hundred,” and the symbol ‘%’ is used to denote this. To convert any fraction to a percentage, you essentially need to find out what that fraction would be if the whole were divided into 100 parts instead of its original denominator.
There are two common methods to convert a fraction like 1/2 to a percentage:
Method 1: Finding an Equivalent Fraction with a Denominator of 100
This method directly applies the definition of a percentage. We have the fraction 1/2. We want to find an equivalent fraction that has a denominator of 100. To change the denominator from 2 to 100, we need to multiply it by 50 (since 2 * 50 = 100). To keep the fraction equivalent (representing the same value), we must also multiply the numerator by the same number, 50.
So, we calculate:
(1 * 50) / (2 * 50) = 50 / 100
Now we have the fraction 50/100. By the definition of percentage, 50/100 means “50 out of 100,” which is written as 50%.
Method 2: Converting to a Decimal First
Another method is to convert the fraction into a decimal first, and then convert the decimal into a percentage. To convert a fraction to a decimal, you divide the numerator by the denominator.
So, for 1/2, we divide 1 by 2:
1 ÷ 2 = 0.5
Now that we have the decimal 0.5, to convert a decimal to a percentage, you multiply the decimal by 100 and add the percentage sign.
0.5 * 100 = 50
Adding the percentage sign gives us 50%.
Both methods demonstrate that 1/2 is equivalent to 50%. Conceptually, this makes perfect sense because 1/2 represents half of a whole, and 50% also represents half of a whole (half of 100 is 50). Therefore, 1/2 is equal to 50%.