Transcript Rational Numbers and Decimals

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
8
.625
8)5.000
- 48
20
-
16
- Add zeros in
the dividend and
continue dividing
until the remainder is 0
40
- 40
0
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 = _________