Rational Numbers and Decimals Essential Question: How can you convert a rational number to a decimal? Unit 1-1

Rational Numbers A rational number is a number that can be written as a ratio of two integers. Neither number can be zero. Example: 4 is a ratio 7 and 0.37 is a rational number because it can be written as 37 which is a ratio. 100 Both are examples of rational numbers.

Vocabulary A ratio is a comparison of two numbers. Example: 3 5 Integers are the sets of whole numbers and there opposites. Example: …-3, -2, -1 , 1, 2, 3…

Vocabulary Continued Corresponding- be compatible, similar or consistent. Conjecture- an opinion or conclusion formed on the basis of incomplete information. Refine-improve by making small changes. Reflect- to seek a deeper understanding.

Equivalent forms To change a ratio to a decimal Divide your numerator (top number) by your denominator (bottom number) Examples: 2 answer would be ?_____ 5 3 4 6 ______ 5 ______

Remember When dividing your numerator by your denominator your answer may be a repeating decimal. It can be written as 0.333…. Or it can be written as 0.3 With the line over the 3 Repeating decimals are rational numbers

Equivalent Forms To change a decimal to a ratio Take your numerator (top number) And place it over 100. Reduce if needed!!! Examples: 0.25 becomes 25 100 --------- 0.17 ______ 0.36 ______ 0.75 _______

Long division Divide the numerator by the denominator. Add a zero after the decimal point. 5 .625 8)5.000 - Add zeros in - 48 the dividend and 20 continue dividing - 16 until the remainder is 0 40 - 40 A terminating decimal is a rational number.

Writing mixed numbers as decimals Change the mixed number to an improper fraction. Keep the denominator Multiply the denominator by the whole number Add the numerator to that number That is your new numerator Divide the numerator by the dominator to get your decimal.

Long division 3 10 Divide 3 by 10. add zero after the decimal point. 3.3 - subtract 9 from10 3)10.0 - you can stop dividing - 9 once you see it is 1.0 repeating. - 9 1

Things to Remember A rational number is a number that can be written a ratio of two integers and neither number can be zero. A rational number that is terminating decimal means it ends. When dividing the remainder is zero. A rational number that has a repeating decimal keep on going and going.

Class work Use your calculator to find the equivalent decimal for each fraction. 1) 2 = _____ 2) 4 = _____ 3) 3 = _____ 5 7 8   4) 7 = _____ 5) 5 = _____ 6) 6 = _____ 12 8 9 _________________________________________ Find the corresponding fraction to each decimal. Remember to write the fraction in simplest form. 7) 0.3 = ______ 8) 0.25 = ______ 9) 0.50 = _____ 10) 0.675 = ______ 11) 0.45 = ______ 12) 0.47 = _________

Name_________________ homework Use your calculator to find the equivalent decimal for each fraction. 1) 3 = _____ 2) 2 = _____ 3) 4 = _____ 6 5 6 4) 7 = _____ 5) 5 = _____ 6) 8 = _____ 10 11 15 _________________________________________ Find the corresponding fraction to each decimal. Remember to write the fraction in simplest form. 7) 0.33 = ______ 8) 0.65 = ______ 9) 0.80 = _____ 10) 0.75 = ______ 11) 0.475 = ______ 12) 0.42 = _________