Rational Numbers and Decimals

1. Rational NumbersandDecimals Essential Question: How can you convert a rational number to a decimal? Unit 1-1

2. 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.

3. 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…

4. 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.

5. 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 ______

6. 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

7. 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 _______

8. 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 0 A terminating decimal is a rational number.

9. 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.

10. 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

11. 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.

12. 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 = _________

13. 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 = _________