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 _________