Decimals, Fractions, and Percents

Definitions Decimal - Any number shown with a decimal point; a number based upon tenths or hundredths. ( 0.2, 0.375, 86.4 ) Fraction - One or more of the equal parts of a whole; a number usually expressed in the form a/b. ( 1/3, 2 5/8, 7/4 ) Percent- The word percent comes from Latin and means “ for each hundred” or “ per hundred.” ( 70%, 6.5%, 4.09% )

Converting Fractions to Decimals To convert a fraction to a decimal, divide the numerator by the denominator. Do this until you get a decimal that terminates or repeats. If it repeats, place a bar (--- ) over the first number that repeats. Example 1: Convert 3/4 to a decimal 3/4 = 3÷4= 0.75 ( terminating decimal) Example 2: Convert 2/3 to a decimal 2/3= 2÷3= 0.66 ( repeating decimal )

Converting Fractions to Percents To convert a fraction to a percent, change the fraction to a decimal ( by dividing the numerator by the denominator ). Then multiply the decimal by 100 and put a percent sign (%). Another way is to move the decimal point two places to the right and put a percent sign (%). Example 1: Convert 1/2 to a percent 1/2= 1÷ 2 = 0.50 0.50x 100= 50.00=50% or 0.50= 0. 5 0= 50% Example 2: Convert 1/3 to a percent 1/3= 1÷3= 0.333 0.333x 100= 33.300=33.3% or 0.333=0. 3 3 3=33.3%

Converting Decimals to Fractions In order to convert a decimal to a fraction, place the number that follows the decimal point over the place that it is in ( tenths, hundredths, thousandths, etc.). Then simplify as necessary. Example 1: Convert 0.7 to a fraction 0.7= 7/10 ( 7 is in the tenths place ) Example 2: Convert 0.25 to a fraction 0.25= 25/100= 1/4 ( 25 is in the hundredths place. 1/4 is the simplified form of 25/100) Example 3: Convert 1.625 to a fraction 1.625= 1 625/1000= 1 5/8 ( 625 is in the thousandths place. 5/8 is the simplified form of 625/1000)

Converting Decimals to Percents In order to convert a decimal to a percent, either multiply the decimal by 100 and write the percent sign (%), or move the decimal point two places to the right and write the percent sign (%). Example 1: Convert 0.20 to a percent 0.20x 100= 20.00= 20% or 0.20= 0. 2 0= 20% Example 2: Convert 4.00 to a percent 4.00= 4.00x 100= 400.00= 400% or 4.00= 4. 0 0=400%

Converting Percents to Fractions When converting percents to fractions, change the percent to a decimal ( divide the percent by 100 or move the decimal point two places to the left ). Then put the numbers behind the decimal point over the place that it is in ( tenths, hundredths, thousandths, etc.). Then simplify as necessary. Example 1: Convert 85% to a fraction 85% = 85÷ 100= 0.85= 85/100= 17/20 ( 85 is in the hundredths place. 17/20 is the simplified form of 85/100 ) Example 2: Convert 12.5% to a fraction 12.5%= 12.5÷ 100= 0.125= 125/1000=1/8 ( 125 is in the thousandths place. 1/8 is the simplified form of 125/1000 )

Converting Percents to Decimals When converting a percent to a decimal, either divide the percent by 100 and put the decimal point, or move the decimal point two places to the left and put the decimal point. Example 1: Convert 72% to a decimal 72%= 72÷ 100= 0.72 or 7 2 . 0= 0.72 Example 2: Convert 62.5% to a decimal 62.5%= 62.5÷ 100= 0.625 or 6 2 . 5= 0.625

Additional Explanations 0.78 or 78/100 or 78% The grid above is divided into 100 equal parts. Of these 100 parts, 78 have been shaded. If we were to write this as a decimal, it would be 0.78; written as a fraction, it would be 78/100; and written as a percent, it would be 78%. All of these, 0.78, 78/100, and 78% are equal. Each one represents 78 parts of the ( whole ) grid. Thus we are able to convert fraction to decimals, decimals to percents, etc.

“Mathematics is the door and key to the sciences.” Roger Bacon 0.75 0.75