Learn about Equivalent Fractions and Decimals In this lesson, let’s learn how to do equivalent fractions and decimals. We will learn how to write the fraction as a decimal and vise versa. We’ll do three problems. First one wants us to write the fraction 3/25 as a decimal. We have to round to the nearest hundredths if necessary okay. So here’s the way you round or you write a fraction as a decimal. If the fraction is a numerator over denominator, we take the numerator and we divide it by the denominator 3 ÷ 25. So, 3 ÷ 25 = 0.12, that’s what we do to convert a fraction to a decimal. If we are converting a decimal to a fraction, .12 to a fraction how would we do it? We have to write the decimal as a fraction in its simplest form. So if the decimal is 0.12, all we have to do is on the top we write down 12 which is the value of the number and the top have two decimal points one, two. So we write down two zeros at the bottom one followed by two zeros. 0.12 is the same as 12/100 which now I can divide by four to get the simplest which gives me 3/25. Is it equivalent to 3/25? Yes. What did I do? We just wrote down .12 as 12/100. Quick lesson, look at how many digits after the decimal point, if it’s two, we put two zeros after the one in the denominator and enumerator we remove zero and the decimal point. 12/100 is the same as 3/25. Let’s see what the third problem says, it says during a football game, Michael completed 15 out of the 18 passes he attempted. So he did 15 out of the 18 passes. Find the completion rate to the nearest thousandth. So we have to convert it to a decimal. 15/18 means I have to divide 15/18. Well I'm going to follow long division. 150, 18 x what goes in 150 let’s say eight, 144. I'm left with 60 so 18 threes are 54, 60 again, 3 60 again and 54 again and I can keep building this right. So it’s basically 0.8333333. This is called the repeating or reoccurring decimal. So if we want our completion rate to the nearest thousandth, thousandth is still here and since after that is a number lower than five, the final answer is 0.833. That’s what we’re looking for. The reason we rounded down is because the digit after that was not five or greater than five.