Fractions, Decimals and Percents Lesson 3.1

Fractions to decimals Numbers can be written in both fraction and decimal form. For example: 3 can be written as 3/1 and 3.0 A fraction illustrates division 1/10 means 1÷10 1/10 in decimal form is .1

Review of decimals 63.165 Fraction 7/10 1/100 19/100 1/1000 23/1000 471/1000 Decimal Each decimal place has a name. Tenths – the first number after the decimal Hundredths – the second number after the decimal Thousandths – the third number in the decimal 63.165

Terminating decimals Decimals that have a definite number of decimal places are called terminating decimals. Examples: 0.1, 0.25, 0.94 These decimals always end.

Repeating decimals When digits repeat themselves forever, they are called repeating decimals. Examples are: 0.333333, 0.754444, 0.121212 Repeating decimals have a bar drawn over the digits that repeat. 4/33 = 0.121212121...can be written as 0.12

Patterns Patterns can occur when we write fractions in decimal form. Example: 1/99 = 0.01, 2/99 = 0.02, 15/99 = 0.15, 43/99 = __________ For fractions with a denominator of 99, the digits in the numerator of the fraction are the repeating digits in the decimal.

Finding the decimal... If I have a fraction with a denominator of 10, the numerator is the decimal to the tenths place. Example: 1/10 = .1 3/10 = .3 7/10 = ________ The decimal is a terminating decimal with one decimal place (the tenths place)

Hundreds... If the fraction has a denominator of 100, the numerator is the decimal to the hundredths place. Example: 26/100 = .26 72/100 = .72 39/100 = ________ If the fraction is less than 10/100, the first number after the decimal is a 0. Example: 7/100 = .07 9/100 = ____________

Thousands... If the denominator is 1000, the numerator is the decimal to the thousandths place. Example: 576/1000 = .576 112/1000 = .112 423/1000 = _________ If the number is less than 100, the first number after the decimal is a 0. Ex. 98/1000 = .098 If the number is less than 10, the first two numbers after the decimal are 0. Ex. 8/1000 = .008

Converting fractions to decimals... What if I get a fraction without a 10, 100, or 1000? First, ask yourself if the denominator can be changed to a 10, 100, or 1000. For example: 1/5 Can the denominator be changed to a 10? YES! Multiply 5 x 2. Then, what you do to bottom, you do to the top! Multiply 1 x 2. Your new fraction is 2/10... What is the decimal value?

Or try this... 20/50 – Can 50 turn into 100? YES! Multiply 50 x 2 = 100, multiply 20 x 2 = 40. New fraction = 40/100... What is the decimal value?

Or how about this? 90/200? Multiply 200 x 5 = 1000 and 90 x 5 = 450 New fraction = 450/1000 What is the decimal?

Find equivalent fractions with denominators of 10, 100 or 1000 for the following fractions. Then, find the decimal value. 6/20 18/25 40/50 60/200

AHH! There is no equivalent! 9/40...I cannot turn this into a fraction with a denominator of 10, 100 or 1000...NOW WHAT?? Remember long division?? Yes, you need to know how.

10/15 We cannot turn 15 into 10, 100 or 1000, so, set up a long division question. Remember, the 15 sits in the nook of the division sign and the 10 sits under the lid. 15√10 15 cannot go into 10, so follow the steps of long division to find your answer.

Division definitions... Divisor – a number by which a number is going to be divided. Dividend – the amount you want to divide up. Quotient – the answer in a division question.

Extra reminder... http://www.wisc- online.com/objects/ViewObject.aspx?ID=ABM 1001 This link will show you the steps of division.

Try converting these fractions to decimals using long division. 4/12 6/15 3/16

Homework Workbook 3.1 Textbook Page 88-90 #2,3,4,5,10,11,REFLECT