1. Rational Numbers and Decimals
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: is a ratio 7
and is a rational number because it can be written as 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: answer would be ?_____ 5
6 ______ ______

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 Reduce if needed!!!
Examples: becomes 25
0.17 ______ ______ 0.75 _______

8. Long division Divide the numerator by the denominator.
Add a zero after the decimal point.
8) Add zeros in
the dividend and
continue dividing
until the remainder is 0 40
- 40
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 subtract 9 from10 3) you can stop dividing - 9 once you see it is 1.0 repeating

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 = _____
4) 7 = _____ 5) 5 = _____ 6) 6 = _____
_________________________________________
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) = ______ ) 0.45 = ______
12) 0.47 = _________

13. Name_________________
homework
Use your calculator to find the equivalent decimal for each fraction.
1) 3 = _____ 2) 2 = _____ 3) 4 = _____
4) 7 = _____ 5) 5 = _____ 6) 8 = _____
_________________________________________
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 = ______ ) = ______
12) 0.42 = _________