Percent and Decimals
What is Percent?
Another way to represent part of a whole is as a percent. Percentages are how much of something you have if the whole is equal to 100. For example, if you had 100 students on a field trip and 63 of them brought a bag lunch, then the percent of them who brought a bag lunch would be 63%. This also works when the whole amount is not 100. If you had 1/4 of a pizza, you could also say that you have 25%. Because 100 divided by four is 25, each quarter of the pizza is 25%.
Don’t forget that you can also have percentages that are greater than 100%. These percentages represent more than one whole thing. If you have one pizza and 1/4 of another, then you could say you have 125% of a pizza. Also, if you invited 100 students on the field trip and 110 show up, you could say you had 110% attendance.
Converting Percent to Decimals
Often to work with a percent, you must convert it to a decimal. This is done by simply moving the decimal point. To convert 63% to a decimal, move the decimal two places to the left to get 0.63. To make 110% into a decimal, move the decimal two spaces to get 1.1.
To make the decimal back into a percent, move the decimal two places to the right. 0.53 becomes 53% and 0.7 becomes 70%.
Converting Decimals to Fractions
To make a decimal into a fraction, count the number of places the numbers go to after the decimal. In the decimal 0.125, the numbers go to the thousandths place (place names begin with tenths after the decimal, then hundredths, thousandths etc.) so the denominator of the fraction will be 1000 and the numerator will be the number in the decimal, 125. The fraction 125/1000 can be reduced to 1/8.
To convert a fraction back into a decimal, divide the numerator by the denominator. If you are using a calculator, the answer should be in decimal form. If you are using long division, keep working the problem out until you have either the end of the decimal or you are in a repeating pattern.
Also, converting decimals to fractions and back can be done by entering them in the calculator and using the toggle key.
Converting Percent to Fractions
Changing a percent to a fraction is done by placing the number of a percent in the numerator position and 100 in the denominator, and then reducing if necessary. 20% would be 20/100, which reduces to 1/5. This works well when the percent is a whole number, but if the percent contains a decimal, you may want to convert the percent to a decimal and follow the instructions for making a decimal into a fraction. If you need to make a fraction into a percent, follow the instructions for making it into a decimal, then move the decimal two places to the right. For 1/4, divide 1 by 4 to get 0.25, then move the decimal to get 25%.
Often you will have word problems that involve percentages. There are actually three values in most percent problems, the percent (also called rate), the whole and the part. If any one of those values is missing, you can find it using the others and this chart:
Finding the Percent
If the percentage is the missing value, the problem will be asking you “what percent.” To know which of the other values is the whole or the part, remember the whole is what you want to find a percent of. The word ‘of’ can be a clue, and even if it’s not used, think about which value the problem wants you to find a percent of. If I have 30 students in a class and 3 of them are absent, what percent are absent? Here we need to find the percent. The number of students in the in the class is the whole because it is what we are finding a percent ‘of.’ Finally, the group that the percent represents in the whole is the part. So, to find the percent, use the chart above and divide the part by the whole. 3 ÷ 30 = 0.1, which converts to 10%.
In cases where the whole is greater than the part, your percent will be more than 100%. In the case of the field trip where 100 were invited and 110 showed up, 100 is the whole because that is the original amount that you want to find a percent of. 110 is the part and your percent is 110%.
Finding the Part
If the part is missing, the problem will ask you what is a certain percent of a number. The number coming after the ‘of’ is the whole. If we were talking about a class of 30 students with 10% absent, how many would be absent? Use the chart above and see that 30 times the percent (you can either put 0.1 or 10% into your calculator) will give you a part of 3.
Finding the Whole
In this case, the number that is missing is the whole, or what the part is a percent ‘of.’ If there are 3 students absent, and they represent 10% of the class, then how many are in the class. Use the chart above to divide 3 by 10% and your answer for the whole should be 30.
Sometimes we are asked to calculate percent change. In these cases, the original number is the whole and the part is the amount it went up or down. For example, if a sweater cost $40 one week, then $50 the next, it increased by $10. The whole in this case is the original amount (40) and the part is the amount of change (10). To find the percent change divide the part by the whole and you will see that it had a 25% increase.
We can also use this for discounts. If a $42 pair of pants were marked 30% off, we could make 42 the whole because it’s the original amount and 30% is the percent. Multiply 30% by 42 and you will get a discount of 12.6 or $12.60. Subtract that from the original price to find our how much you have to pay. 42 – 12.60 = 29.4 or $29.40
Interest is the amount of money you pay to borrow money. It’s rent for holding on to someone else’s money. It can also be money you get paid for letting someone hold on to your money, as is in the case of an investment. The interest is calculated using an interest rate, which is a percent. The formula for calculating interest is I=PRT where I is the amount of interest; P is the principle, or amount of money borrowed; R is the rate, written as a percent; and T is the amount of time in years.
If you finance $10,000 for a car, and you keep the loan for five years at 5% interest, you would calculate your total interest paid by filling in the formula 10000 × 5% × 5 = $2500 in interest.