Space tourism is a multibillion dollar industry.
For a price of $20 million, a civilian can travel
on a rocket or space shuttle and visit the
International Space Station for a week.
a)What would $20 million look like when written
out?
b)What would you have to multiply $2 by to get to
$20 million?
c)How can you write 10,000,000 as a power of
10?
Lesson 7-2
Writing a number in
scientific notation
improves efficiency and
accuracy of various
calculations involving
VERY LARGE and VERY
SMALL numbers.
Vocabulary
Scientific notation is a shorthand way to
write numbers using powers of 10.
a 10 where 1  a  9
n
Examples:
8.3 x 105
4.12 x 1022
7.1 x 10-5
Standard notation is a number written with
place values.
Examples:
152
9.5
0.085
Problem 1: Recognizing Scientific
Notation
Is the number written in scientific notation? If not, explain.
1) 0.23 x 10-3
3) 9.3 x 1009
2) 2.3 x 107
Conditions:
•1st factor is between 1 and 9
•2nd factor is a power of 10
Got it?
Is the number written in scientific notation? If not, explain.
4) 53 x 104
5) 3.42 x 10-7
6) 0.35 x 100
Scientific Form  Standard Form
The exponent tells you how many places to move the decimal
point.
If there is a positive exponent, move the decimal place
to the ________.
If an exponent is positive, a number gets ____________.
If there is a negative exponent, move the decimal place
to the _________.
If an exponent is negative, a number gets ______________.
Scientific Notation to Standard Form
1. Express 6.49 × 105 in standard form.
Scientific Notation to Standard Form
2. Express 1.8 × 10–2 in standard form.
3. Express 3.16 × 10–2 in standard notation.
4. Express 7.61 × 103 in standard notation.
Standard Form  Scientific Form
1) Move the decimal after the first whole number
(1, 2, 3, 4, 5, 6, 7, 8, 9).
2) Add your multiplication sign and base (x 10)
3) The number of moves between the original and
the new decimal place will be the exponent.
•
If the original number is greater than one,
the exponent will be ___________.
•
If the original number is less than one, the
exponent will be ___________.
Standard Form to Scientific Notation
1. Express 4,062,000,000,000 in scientific notation.
Standard Form to Scientific Notation
2. Express 0.000000823 in scientific notation.
3. Express 458,000,000 in scientific notation.
4. Express 0.0000452 in scientific notation.
Multiply and Dividing in Scientific Notation
• When you multiply in scientific notation,
just multiply the first factor and
_________ the exponents.
• When you divide in scientific notation, just
divide the first factor and _________ the
exponents.
Multiply with Scientific Notation
1. Evaluate (5 × 10–6)(2.3 × 1012). Express the result in
both scientific notation and standard form.
Divide with Scientific Notation
2. Evaluate
. Express the result in both
scientific notation and standard form.
3. Evaluate (8 × 105)(2.1 × 10–3). Express the result in
both scientific notation and standard form.
4. Evaluate
Express the result in both
scientific notation and standard form.