6.2 Operations with Scientific Notation
Scientific notation is a way to write very large or very
small numbers.
In scientific notation, a number greater than or equal to 1
and less than 10 is multiplied by an integer power of 10.
decimal x 10exponent
Review Question
Write 3.5 × 10 in decimal form.
Pull
4
1
Answer?
Review Question
Pull
Write 0.000784 in scientific notation.
2
Answer?
In 2000, an estimated 7.7 x 107 people spoke French as their first
language and an estimated 1 x 108 people spoke German as their first
language. Which language had more speakers? How many more?
In 2000, and estimated 1.664 x 108 dollars in 1000-dollar bills
were in circulation. How many 1000-dollar bills were in
circulation in 2000?
3 Answer?
es)
Scientific Notation:
Simplify:
(1.2×10 )(4.0×10 )
Pull
15
-3
Scientific Notation:
Simplify:
(8 ×105)(2.4×10 )
Pull
8
Scientific Notation:
Simplify:
(1.2×1011)(9.0×10 )
Pull
7
You try:
Simplify:
(7 ×1015)(3 ×10 )
8
(1.7 ×10-8)(2 ×10 )
13
Divide 2.4 x 103 by 4 x 105 by first writing the numbers in standard form
and then multiplying. Write your answer in scientific form. Look at the
exponent in your divisor and your dividend and compare them to the
exponent in the quotient. What do you notice?
Scientific Notation:
Simplify:
(36 ×1011)/(9.0×10 )
Pull
7
Scientific Notation:
Simplify:
(7.2×105)/(8 ×10 )
Pull
3
Scientific Notation:
Simplify:
(3.2×107)/(8 ×10 )
Pull
11
You try:
Simplify:
(9.6×1013)/(1.2 ×10 )
11
(4.8×109)/(6 ×10 )
17
Scientific Notation:
Simplify:
Pull
(9 ×1013)2
Scientific Notation:
Simplify:
Pull
(2 ×105)3
Scientific Notation:
Simplify:
Pull
(2 ×107)-2
You try:
Simplify:
(5 ×1012)3
(3 ×108)3
5,000,000,000 ⋅ 45,670,000
Pull
n.
Scientific Notation:
0.000000076 ⋅ 0.0000643
Pull
n.
Review Question
76
of the US was 2.7 × 107.
What percent of the world
population was the US
population?
Pull
6
Scientific Notation Example:
In 1998, the population of the
world was about 5.9 billion. In
the same year, the population