Transcript Write the following numbers in scientific notation.

Exponents of Ten
What Is the Standard Form
of These Tens?
2
100
10
3
1,000
10
4
10,000
10
5
10
100,000
Multiplying Multiples of Ten
Multiply These Numbers
100 x 2 =
200
1,000 x 3 =
3,000
10,000 x 7 = 70,000
100,000 x 9 = 900,000
Combine these two steps for
writing large numbers.
2
6 x 10 = 600
6 x (10 x 10) = 6 x 100 = 600
What is the Standard
Number?
2
7 x 10 = 700
What is the Standard
Number?
3
8 x 10 = 8,000
What is the Standard
Number?
4
9 x 10 = 90,000
What is the Exponent Form?
500 = 5 x 10
2
What is the Exponent Form?
3
6,000 = 6 x 10
What is the Exponent Form?
4
90,000 = 9 x 10
Write the following number in decimal form.
5.75 x10
4
This expression can be rewritten as 5.75 x10 x10 x10 x10
Furthermore
5.75 x10 x10 x10 x10  ( 5.75 x10 ) x10 x10 x10
 ( 57.5 ) x10 x10 x10
 ( 57.5 x10 ) x10 x10
 ( 575 ) x10 x10
 ( 575 x10 ) x10
 5750 x10
 57500
Positive powers of 10 – When the exponent (n) is
positive, move the decimal point to the right the same
number of places as the exponent. Add zeros when digits
are not present.
Write the following
numbers in decimal form:
a.
b.
c.
7.41x10
Solutions
1
a. 74.1
0
b. 3.99
3.99x10
8.663x10
4
c. 86630
Write the following number in decimal form.
7.86 x10
2
 1
This expression can be rewritten as: 7.86 x 
 10 
Furthermore,
2
 1
 1  1
7.86 x   7.86 x  x 
 10 
 10   10 
1  1

  7.86 x  x 

10   10 
 0.786 x
 0.0786
1
10
2
Negative powers of 10 – When the exponent (n) is negative,
move the decimal point to the left the same number of places as
the absolute value exponent. Add zeros when digits are not
present.
Write the following
numbers in decimal form:
a.
b.
c.
3.24 x10 2
9.1x10
Solutions
a. 0.0324
5
b. 0.000091
1
c. 0.56
5.6 x10
1) Move the decimal point to the right or left
until you have a number that is greater than or
equal to 1, but less than 10.
2) Count how many places you moved the
decimal point. This number will become the
absolute value of the exponent.
3) If you moved the decimal point to the left, the
exponent will be positive.
4) If you moved the decimal point to the right,
make the exponent negative.
Write the following numbers
in scientific notation.
a.
b.
1043
2.5
c.
0.000495
Solutions
a.
b.
c.
3
1.043x10
0
2.5 x10
4.95 x10 4
a. The decimal is to the right of the 3. Move it left 3 places.
b. This number is already greater than or equal to one and less
than 10. Therefore, the decimal doesn’t have to be moved
and the exponent will be 0
c. Move the decimal right 4 places.
Altering Exponents
• Making the # BIGGER makes the exponent
0.00356 x 104 
The number needs to
be bigger by 3 places.
smaller.
3.56 x 101
So we subtract 3
from the exponent.
• Making the # smaller makes the exponent BIGGER.
698.09 x 104  6.9809 x 106
The number needs to
be smaller by 2 places.
So we add 2 to
the exponent.
Use a calculator to perform the indicated operation. Write your
result in correct scientific notation.
3
5
( 9.1x10 ) x ( 4.2x10 )
1) Enter 9.1 in your calculator.
2) Press the key marked EXP or EE on your calculator. If
this is written above another key, then you will have to
press SHIFT or 2nd before pressing the EXP or EE key.
3) Enter the value of the exponent.
4) Press the times key.
5) Enter 4.2
6) Repeat steps 2 and 3.
7) Press Enter or =. You should get 3.822x10-1
Multiply (3.45 x 107) x (6.25 x 105)
Enter into your calculator:
( 3.45 EXP 7 ) * ( 6.25 EXP 5 ) =
21562500000000
Convert to scientific notation:
2.16 x 1013
=
3.1 x 1010
2) (2.0 x 10 -1) x (8.5 x 105) =
1.7 x 105
1) (6.8 x
103)
x (4.54 x
106)
3) (4.42 x 10-3) x (4 x 10-2) =
1.7 x 10-4
Divide 3.5 x 108 by 6.6 x 104
Enter into your calculator:
( 3.5 EXP 8 ) ÷ ( 6.6 EXP 4 ) =
5303.0303030303
Put into scientific notation:
5.3 x 103
1) divide (2.4 x 10 6) by (5.49 x 10-9)=
4.4 x 1014
2) divide (9.2 x 10-3) by (6.3 x 106) =
1.5 x 10-9
3) divide (1.92 x 10-2) by (2.3 x 106) =
8.3 x 10-9
Add 3.76 x 104 and 5.5 x 102
Enter into your calculator:
( 3.76 EXP 4 ) + ( 5.5 EXP 2 ) =
38150
Put in scientific notation:
3.82 x 104
1) (3.95 x 105) + (7.8 x 103) =
2) (2 x
10-3)
3) (6.423 x
+ (8 x
101)
10-4)
=
+ (5.001 x
4.028 x 105
2.8 x 10-3
10-1)=
6.473 x101
Subtract (4.8 x 105) - (9.7 x 104)
Enter into your calculator:
( 4.8 EXP 5 ) - ( 9.7 EXP 4 ) =
479990.3
Put in correct scientific notation:
3.8 x 105
1) (4.54 x 107) - (1.01 x 108) =
2) (8.23 x 104) - (3.02 x 105) =
3) (7.83 x
10-2)
- (2.20 x
10-3)
=
-5.56 x107
-2.20 x 10-5
7.61 x 10-2