Math 123 - Section 5.7 - Negative Exponents and Scientific Notation- Part II - Page 1
Section 5.7
Negative Exponents and Scientific Notation - Part II
I.
Scientific Notation
A.
A number is in scientific notation when it looks like:
n x 10r
where
1.
1 < n < 10 (i.e. – n has only one digit to the left of the decimal point.)
2.
r is the number of places the decimal point had to be moved in the original
number to get n.
a. r is positive if we moved to the left
b. r is negative if we moved to the right
B. Examples – Write each number in Scientific Notation.
1. 602,000,000,000,000,000,000,000
Answer: 6.02 x 1023
2. 0.0000000000000000001025
Answer: 1.025 x 10-19
3. Now you try one: 150,000,000,000,000,000,000
Answer: 1.5 x 1020
4. Try another one: 0.0000000000005
Answer: 5 x 10-13
C. Changing to Standard Notation
1. Move the decimal point the number of places that the exponent of ten is.
2. Move the decimal point to the left if the exponent is negative.
3. Move the decimal point to the right if the exponent is positive.
D. Examples – Write in Standard Notation
1. 8 x 104
Since the exponent is positive, we will move the decimal point 4 places to the
right to get:
Answer: 80,000
2. 4.5 x 10-6
Since the exponent is negative, we will move the decimal point 6 places to the
left to get:
Answer: 0.0000045
3. Now you try one: 9.64 x 10-7
Answer: 0.000000964
4. Try another: 7.3 x 108
Answer: 730,000,000
II.
Scientific Notation and a Calculator
A.
On your calculators, you should see either an
B.
To input 6.02 x 1023 on your calculator, press:
1.
6.02
2. EE
or Exp
EE
or Exp
© Copyright 2012 by John Fetcho. All rights reserved
key.
Math 123 - Section 5.7 - Negative Exponents and Scientific Notation- Part II - Page 2
3.
C.
III.
23
To input 1.025 x 10-19 on your calculator, press:
1.
1.025
2.
or Exp
EE
3.
(-)
4.
19
or
+/ -
Multiplication and Division
A.
We will treat this similarly to how we treated exponential expressions.
1.
We will multiply the coefficients and add the exponents when we multiply.
2.
We will divide the coefficients and subtract the exponents when we divide.
B.
Examples - Perform the indicated operations.
1.
(15 x 108) x (20 x 1010)
Since we are multiplying, we will multiply the coefficients (15 and 20) and add
the exponents (8 and 10). But note that the base of the exponents will remain
the same, namely 10:
(15  20)(108+10)
OR
300 x 1018
But this is not in scientific notation (why not?). So to get this into scientific
notation, we need to make the coefficient have just one digit to the left of the
decimal point. Since we will be moving the decimal point two place to the left,
we will add two to the exponent on the 10.
Answer:
3 x 1020
2.
1x1025
5 x1010
Here we are dividing, so we will divide the coefficients and subtract the
exponents:
1
25-10
)
  x (10
5
OR
.2 x 1015
But this is not in scientific notation (why not?). To get it into scientific notation,
we will move the decimal point one place to the right. This also means that
we need to subtract one from the exponent on the 10.
Answer:
2 x 1014
3.
Now you try one:
Answer:
6 x 10-12
C.
(3 x 10-4) x (2 x 10-8)
On the Calculator
1.
We will input the numbers the same as before, except now we will inputting
two numbers at a time with an operation in between.
2.
Your answer will be output in scientific notation, but it will not have a “x 10” in
it. When you write your answer on your paper, you will need to interpret what
your calculator has and put in the “x 10”. Answers such as
a.
2 E 14 or
b.
214
are NOT acceptable.
© Copyright 2012 by John Fetcho. All rights reserved
Math 123 - Section 5.7 - Negative Exponents and Scientific Notation- Part II - Page 3
D.
1.
Examples - Perform the indicated operations.
(1.5 x 109) x (2 x 1011)
Input into your calculator
a.
1.5
b.
or Exp
EE
c.
d.
e.
f.
g.
h.
9
x (for multiply)
2
or Exp
EE
11
=
or
Enter
Your calculator will output either
3 E 20 or 3 20
You need to interpret this. It really means:
Answer:
3 x 1020
2.
Now you try one:
Answer:
3.
3 x 105
9 x1015
3 x1010
Note that in scientific notation, negative exponents are ok.
© Copyright 2012 by John Fetcho. All rights reserved