How to Represent Fractions and Decimals as Percents In this lesson, let’s talk about fractions and decimals and how we convert them to percent values. We’ll use two problems. Let’s do the first one. First problem says, at a party a chocolate cake was divided between Samantha and Mike. Samantha ate 3/5 of the cake and Mike ate 0.4 of the cake. We need to find what percentage of the cake did Samantha and Mike individually eat. So essentially what we have to do is we have to convert or write 3/5 and 0.4 in percent values. So, let’s see how we do that. Let’ stake them one by one. Let’s do the first part which 3/5 as percent. What is a percent? Well, percent is a special ratio where the denominator equals 100. It’s actually a ratio where the denominator equals a hundred. So, in order to represent 3/5 as a percent, what that means is 3/5, we need to write this down as something with the denominator is 100. So, let’s say the value of the numerator should be n. So if this is true, if 3/5 needs to be written as n/100, these are equivalent fractions. So if that’s the case, the cross product must be equal. If the cross product’s equal that means 3 x 100=5 x n. I’m going to divide both sides by five so that I can have n alone on the right hand side. So, this leave us with n and this gives us 3 x 100 is 300/5, which gives me, if n=300/5, 300/5 is 60 so n is 60. If n is 60, when we represent this as a percent, that means 3/5=60/100 or 60%, so that’s the first piece that we’ve got to do. Now, let’s look at the second one which is we’ve got to convert 0.4 in percent. So, the second part is 0.4 in percent. We will do the same thing. 0.4 is a decimal value. Well 0.4, I can write as a fraction by saying this is 4/10. And the way we do that is if there’s one digit to the right of the decimal point, we have the denominator be one followed by as many zeroes as there are digits after the decimal point. Since there was only one digit, it’s 4/10 and we ignore the decimals on top. 4/10 is a fraction, so I just learned how to convert a fraction to a percent. So, let’s apply the same model. 4/10, if I have to write this as a percent, that means this is n/100. We need to find n. We can do that by cross multiplying, 4 x 100=10 x n. I’m going to divide both sides by 10 so I can have n being alone on the left and divided it by 10, so that’s 4 x 100 is 400/10=n, 400/10 is 40, so 0.4=40%. Now that I have these two, well we have the answer. We were suppose to know what percent of cake did Samantha eat if she ate 3/5, Samantha ate 60% of the cake and Mike on the other hand ate 0.4 which means Mike ate 40% of the cake. That’s the first question. Now, let’s go back and look at the second one. The US nickel was once made with 100% nickel. Today’s nickels are three parts copper and one part nickel. What percentage of today’s nickel is pure nickel? So, we are given that today’s nickels are three parts copper and one part nickel. Today’s nickels are three parts copper and one part nickel. We need to find what percentage is nickel, that’s what we need to find. So, what we know is, total number of parts in today’s nickel equals three parts copper, one part nickel so it’s four which is 3+1 by the way. So, the total number of parts is four. What does that mean? Well, parts that are copper are three and parts that are nickel are one, that’s what’s been given to us. So, total parts equals four; three parts of copper, one part on nickel. So, what is the fraction of the nickel? Fraction of today’s nickel which is actually made up of nickel equals one part out of four. What we need to do is find the percent value of that, so we need ¼ as a percent. How do we do that? Well 1/4, if I want to convert it to a percent will equal to n/100 because ratio or ¼ is a fraction and if it needs to be expressed as a percent, a percent is a fraction with a numerator as the percent value and the denominator as 100. So this is equal, their cross multiplications equal which means 1 x 100 which i