Vocabulary
All whole numbers except zero are the __________ numbers, also known as "counting numbers"
Natural
9/25
0.36 Terminating after 2 digits
-2 9/10
-2.9
-55/18
-3.0555... (5 repeats)
-2 3/7
RATIONAL (it's a ratio of 2 integers; AKA a FRACTION!)
Numbers including 0, 1, 2, 3, 4, 5 .....
Doesn't include fractions, decimals, or negative rational numbers.
Whole numbers
-2 5/8
-2.625 Terminating after 3 digits
11 1/6
11.166... Repeats at the second digit; bar notation over the 6
Maggie bought 11/3 lb of apples to make some apple pies. What is the weight of the apples written as a decimal?
3.666...lbs (6 repeats)
3.141592653589....
NOT RATIONAL (It's Pi!)
Any number that can be written as a ratio of 2 integers and doesn't have a divisor or denominator of 0.
Rational number
155/7
22.142857142857... Repeating after 6 digits; bar notation over 142857
-8 2/5
-8.4
Harry's dog weigh 103/8 pounds. What is the weight of Harry's dog written as a decimal?
12.875 lbs
58/27
RATIONAL (any ratio of 2 integers is rational)
All whole numbers and their opposites including zero.
Integers
-14/11
-1.27 (bar notation over the 27) Repeating
-7 1/4
-7.25
The water level dropped 23/11 meters. Convert the change in water level to a decimal.
-2.0909...m (bar notation over 09)
12.120120012000....
An integer, that is not positive or negative. This integer is it's own opposite!
ZERO
12/13
.923076... (bar notation over all 6 digits) Repeating
54 3/24
54.125
The temperature rose 89/27 degrees Fahrenheit between 8 am and 12 pm on Sunday. What was the change in temperature during this time in decimal form?
3.296 (bar notation over 296) degrees Fahrenheit
Tom is trying to write 3/47 as a decimal. He used long division and divided until he got the quotient 0.0638297872, at which point he stopped. Since the decimal doesn't seem to terminate or repeat, he concluded that 3/47 is not rational. Do you agree or disagree? Why?
Disagree; the definition of a rational number is a number that can be written as a ratio of two integers with a denominator not equal to zero, which describes 3/47. Tom would need to keep dividing to find a repeating pattern or have the decimal terminate. It will eventually repeat since the divisor doesn't have a factor of 2 &/or 5!