Real Numbers Worksheet Page 2
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1
2
3
41 (zero power rule)
2.
3.
(quotient rule)
(negative power rule)
4.
∙
5.
(power of power rule)
Ex 1: a. 3 ∙ 3
3
3
243.
b. 100
1.
5
5
25.
c.
d. 3
.
∙
e. 2
2
2
1024.
9
A positive exponent tells how many zeros follow the 1. For example, 10
, is a 1 followed by 9
zeros: 1,000,000,000.
A negative exponent tells how many places there are to the right of the decimal point. For
-9
example, 10
has nine places to the right of the decimal point.
-9
10
= 0.000000001
A positive number is written in scientific notation when it is expressed in the form
a 10
n
,
where a is a number greater than or equal to 1 and less than 10 (1 ≤ a < 10), and n is an integer.
Convert Scientific Notation to Decimal Notation:
If n is positive, move the decimal point in a to the right n places.
If n is negative, move the decimal point in a to the left |n| places.
Ex 2: a. 3.5
10
3,500,000.
b. 3.5
10
0.0000035.
Converting From Decimal to Scientific Notation( to write the number in the form a 10
n
):
•
Determine a, the numerical factor. Move the decimal point in the given number to obtain
a number greater than or equal to 1 and less than 10.
•
Determine n, the exponent on 10
n
. The absolute value of n is the number of places the
decimal point was moved. The exponent n is positive if the given number is greater than
or equal to 10 and negative if the given number is between 0 and 1.
Ex 3: a. 34,600,000
3.46
10 .
b. 0.0000123
1.23
10 .
We use the product rule for exponents to multiply numbers in scientific notation:
(a 10
) (b 10
) = (a b) 10
n
m
n+m
Add the exponents on 10 and multiply the other parts of the numbers separately.
Ex 4: 2.6
10
∙ 1.43
10
2.6 ∙ 1.43
10
3.718
10 .
We use the quotient rule for exponents to divide numbers in scientific notation:
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