Classify the decimal expansion of each fraction as a terminating decimal or a repeating decimal.
2 answers:
A repeating decimal is a decimal that has a digit, or a group of digits, that repeat forever. A terminating decimal, on the other hand, is a decimal that ends. To find which decimals are repeating and which ones are terminal, we are going to simplify our fractions, and express them in decimal form:
6 is repeating forever, so this is a repeating decimal.
3 is repeating forever, so this is a repeating decimal.
45 is repeating forever, so this is a repeating decimal.
No digit is repeating forever, so this is a terminating decimal.
We can conclude that:
Repeating decimals:
, 
, and 
Terminating decimals:
We can conclude that:
Repeating decimals:
Terminating decimals:
You might be interested in
Answer:
Graph dots in the points of the following:
(-4,10)
(-3,8)
(-2,6)
(-1,4)
(0,2)
(1,0)
(2,-2)
(3,-4)
(4,-6)
(5,-8)
(6,-10)
Connect these dots to make a line.
Answer:
C,
Step-by-step explanation:
To remind you, Euler's formula gives a link between trigonometric and exponential functions in a very profound way:
Given the complex number , we want to try to get it in the same form as the right side of Euler's formula. As things are, though, we're unable to, and the reason for that has to do with the fact that both the sine and cosine functions are bound between the values 1 and -1, and 2√2 and -2√2 both lie outside that range.
One thing we could try would be to factor out a 2 to reduce both of those terms, giving us the expression
Still no good. √2 and -√2 are still greater than 1 and less than -1 respectively, so we'll have to reduce them a little more. With some clever thinking, you could factor out another 2, giving us the expression , and <em>now </em>we have something to work with.
Looking back at Euler's formula , we can map our expression inside the parentheses to the one on the right side of the formula, giving us
and
, or equivalently:
At this point, we can look at the unit circle (attached) to see the angle satisfying these two values for sine and cosine is 7π/4, so , and we can finally replace our expression in parentheses with its exponential equivalent:
Which is c on the multiple choice section.
