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1 Math 84 Activity #2 Your Name: Percents Converting Between Decimals, Fractions, and Percents "Percent" is actually "per cent", meaning "out of one hundred". You can use this fact, along with the fact that fractions mean division, to convert between fractions, percents, and decimals. * Percent means parts per 00. In this figure there are 9 of the 00 parts shaded ( Thus, 9% is shaded. Percentages refer to fractions of a whole; that is, whatever you're looking at, the percentage is how much of the whole thing you have ). For instance, 50% means or or / 2 of one whole. 25% means / 4 - Demonstrate why this is true. 40% means 2 / 5 Demonstrate why this is true. Converting Fractions to percents: Ex. 2 If you divide by 2 the result is 0.5 (a terminating decimal),.5 2.0, or 50% So, perform the division which the fraction bar indicates. Then multiply by 00 and add the percent sign (or move the decimal point to the right two places). Here's a messier example that you won't have memorized:

2 This is a non-repeating, non-terminating decimal. Note that the remainder is 0 and the divisor is 35, so you'll be appending " 0 / 35 " to the "0.54": NOTE!: Alternative way for converting fractions to percent 9 35 = 9 00% % 380 % 2 54 % So what happens to numbers as they convert from decimals to percents, to fractions, to decimals? A. What changes happen below, if you were describing them? (note the decimal). % = 00 = 0.0 From % to fraction? % to Decimal? B. What changes happen below, if you were describing them? (note the decimal) = 2% = 2 From decimal to % 00 Percent to fraction?

3 What percent is shaded? /00 = % What percent is shaded? /00 = % Simplify the fraction What is this number as a decimal? Simplify the fraction What is this number as a decimal? Stump your partner. Shade in squares (or partial squares. What percent is shaded? /00 = % Simplify the fraction

4 What is this number as a decimal? TOOLKIT Percents to Fractions Because % =, any % can be 00 converted to a fraction by dividing by Easy Ex: 44% = = = % = = = = Tougher Ex: 6.5% = 2 (two choices; 00 multiply by the reciprocal or use the multiplier and clear fractions a. 2 3 = = or... clear fractions w / multiplier ( 2) 2 3 b. = (2 is the multiplier) ( 2) Last example: fffffffffffffffffffffffffffffffffffffffffffff2 Percents to Decimals Omit the % symbol and divide by 00. Move decimal point two places to the left. Ex: 5% = 5/00 =.05 04% = 04.(%) =.04 Decimals to Percents. Multiply by 00 (move decimal two places to the right!), add % symbol. Ex: = (0.025x00)% = 2.5% 2.34 = 234% = 0.9% Decimal to Fraction - Any terminating decimal can be converted to a fraction by counting the number of decimal places, and putting the decimal's digits over followed by the appropriate number of zeroes. For example: Fractions to Percents - Convert to decimal. Multiply by 00. Ex: Ex: = 0.35 ( )% 35% Ex: = 00% = % = % = 3 % or 3.5% Fraction to Decimal Divide! If you remember that fractions mean division, then this is easy. The calculator can do the work for you, because you can just have it do the division.

5 Problems to practice!. If a class has 26 students, and 4 are female, what percentage of the students are female? 2. Convert to a fraction. 3. Convert the following decimals to percents. a b c. 0.9 d Convert the following fractions to percent by first converting to decimals. a. 20 b. 2 3 c. 5 d Convert the following percents to decimals. a. 3% b. 6.5% c. 5 ½% d. 0.5% 6. Convert the following percents to fractions. a. 05% b. 300% c. 6.5% d % 3

6 Write your own Review: Come up with a real life percent problem (a word problem) which you might encounter or have encountered. Write the math question for it (see top of next page). Write the equation for it. Solve it. Don t make it too hard! Problem: Math Question: Equation: Solution: Rules to remember : Percent x Base = Amount (PB=A). Find the math question in each problem. Problem: I owe % tax for a $20.00 sweater. What is my total owed? Example:. What is % of 20? is a math question easy to convert to an equation. X = 0.0 x 20 ( what = x, % = 0.0, of indicates to multiply. Solve for x. X =.4 Or. as a proportion problem: x = (cross multiply) 20 = 00 x (solve for x). Find 5.% of What is % of 66? 9. What percent of is 88? Equation Solution

7 0. Your hourly wage was $2.50 before your pay raise of 8%. What is your new hourly wage? (using words, what is the math question?) Equation Solution. You bought a car for $4,500 and paid $900 in taxes. What percent did you pay in taxes? Math question Equation Solution 2. Spencer made 8 out of the 2 shots he took at last night s game. What percentage did he miss? Math question Equation Solution 3. Complete the table. Fraction Decimal Percent a. 3 8 b c. 83 % 3 d. 0.05