Percents to Decimals and Fractions
So on this problem, 51.2% of the students at Ridgemont School scored above average in a fitness test. How can this percent be written as a decimal and as a fraction in simplest form?
So in this problem, we need to write 51.2% as a decimal. So to do that, let’s follow these steps. So, the first step is we need to write the percent as a fraction and the fraction has to have the denominator of 100. So, we’re going to take 51.2% and turn it into a fraction. So, we’re going it as a fraction so it will be 51.2/100. Now our second step is to remove the decimal from the numerator. So to do that, we’re going to multiply the numerator and the denominator by the same power of 10. So, we’re going to multiply 51.2 and 100 by 10. So, we’re going to take 51.2 and multiply that by 10 and we’re going to take 100 and multiply that by 10. So, what we get is 51 or 512/1000.
Now, our next step is to write an equivalent decimal. So now, we have to write an equivalent decimal for 512/1000. So, when we write 512/1000 it is read as five-hundred thousandths. So, we know it’s in the thousandths place. Now to divide by a thousand, we’re going to take 512 and divide it by 1000. And when you divide it by 1000, you move a the decimal point three places to the left. So if the decimal point is here, you move it three places to the left. So then, it would be 0.512. So, 51.2% written as a decimal would be written as 512/1000.
Now, the second part of this problem is to write as a fraction. So, if we want to write 51.2% as a fraction, we’re going to use these steps. So, the first thing is to write the percent as a fraction so that the numerator has no decimal. So, you want the numerator has no decimal. So to do that, we’re going to start of with 51.2% equals and so that would be 51.2/100, then remember we said, if we multiply it by 10, we can take away the decimal. So, we’re going to multiply it by 10, so we get 512/1000. So now, we’ve written the percent as a fraction where the numerator has no decimal.
Now, our second step is to simplify the fraction. So to simplify a fraction, we need to divide the numerator and the denominator by the greatest common factor. So, the greatest common factor for 512 and 1000 is eight. So, we’re going to divide 512 by eight and then we’re going to divide 1000 by eight. And when do that, we get 64/125. So, 51.2% can be written as a fraction and it would be 64/125. So, this is in fraction form.
So, some things to keep in mind and remember is that a percent can be written as a decimal and as in fractions. So to write a percent as decimal, we write the percent as a fraction first with the denominator of a hundred and then we remove the decimal from the numerator and then you write an equivalent decimal. Now, to write a percent as a fraction, we write the percent as a fraction so that the numerator has no decimal and then we simplify.
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