Expanded Notation of 1,000 = (1 x 1000) + (0 x 100) + (0 x 10) + (0 x 1).
Number (expanded) notation: (4 x 10,000,000) + (8 x 1,000,000) + (0 x 100,000) + (0 x 10,000) + (0 x 1,000) + (0 x 100) + (0 x 10) + (0 x 1)Word notation: forty eight-million thousand
2.1 = 2.1 E^0 E means 'x 10' and 10^0 equals 1 Therefore 2.1E^0 = 2.1
Expanded Notation of 100 = (1 x 100) + (0 x 10) + (0 x 1)
Expanded (number) Notation of 85,000,000 = (8 x 10,000,000) + (5 x 1,000,000) + (0 x 100,000) + (0 x 10,000) + (0 x 1,000) + (0 x 100) + (0 x 10) + (0 x 1)85,000,000 written in word notation is: 85,000,000 = eighty five-million thousand
[0, x] assuming both 0 and x are included. If neither are included it would be (0, x). If 0 is included but x is not then it is [0, x). If x is included but 0 is not then it is (0, x].
0 < x < +INF is the same as: (0, +INF)
Positive: (0, infinity)Nonnegative: [0, infinity)Negative: (-infinity, 0)Nonpositive (-infinity, 0]
f(x) is decreasing on the interval on which f'(x) is negative. So we want: (x2-2)/x<0 For this to be true either the numerator or the denominator (but not both) must be negative. On the interval x>0, the numerator is negative for 0<x<sqrt(2) and the denominator is positive for all x>0. On the interval x<0, the denominator is negative for all values on this interval. The numerator is positive on this interval for x<-sqrt(2). So, f' is negative (and f is decreasing) on the intervals: (-infinity, -sqrt(2)), (0, sqrt(2))
X = (-infinity, 0) U (0, infinity) The above is read as X equals negative infinity, comma zero, union, zero, comma infinity on an open interval (By the way, this interval is made up of two intervals). A parenthesis by a value indicates it is not included. This means X could equal anything between -infinity and 0 and X can equal anything between 0 and infinity. X can not equal -infinity. X can not equal 0. X can not equal infinity. The interval is open because none of the starting or ending values can be a value of X (It's a parenthesis by all the starting and ending values). There is a parenthesis by 0 because 0 is not a possible value of X (the question says so). There is a parenthesis by -infinity and infinity because they are not real numbers. So whether either of them is included in the answer, they always have a parenthesis by them. If a number was included in an interval, there would be a square bracket by it, like this: [ or ]. If the starting number and the ending number on the interval is included then the interval is closed.
32
Scientific Notation: 3 × 10^8Expanded Notation: (3 x 100000000) + (0 x 10000000) + (0 x 1000000) + (0 x 100000) + (0 x 10000) + (0 x 1000) + (0 x 100) + (0 x 10) + (0 x 1)
First, 10 x 10 = 100 Second, e^0 = 1 (exponential zero equals one) Therefore, 100 x e^0 = 100 x 1 = 100 Answer: the exponential notation of 10 x 10 is therefore: 100e^0
That is, 0
(0, infinity) Note that you should use the infinity sign instead of the word (the sideways 8).
Expanded Notation of 1,000 = (1 x 1000) + (0 x 100) + (0 x 10) + (0 x 1).
Number (expanded) notation: (4 x 10,000,000) + (8 x 1,000,000) + (0 x 100,000) + (0 x 10,000) + (0 x 1,000) + (0 x 100) + (0 x 10) + (0 x 1)Word notation: forty eight-million thousand