#### Transcript Warm up

```Warm up
1. If you invest \$1,000 at 7% for 2 years. How much
will you have after two years if it compounds
annually?
\$1144.90
2. How much money should I save in an account paying
10% interest compounded yearly if I want to have \$484 in
2 years?
\$400
Scientific Notation
TSWBAT:
• Write numbers in scientific notation
• Write numbers in standard form from
scientific notation
• Add and Subtract numbers in
Scientific Notation
• Multiply and Divide numbers in
Scientific Notation
We use scientific notation as a
shorter way of writing really big
numbers (or really tiny numbers).
1) You have over
3,750,000,000,000,000,000
2) The influenza virus is about
0.00000001 meters in diameter.
What does Scientific
Notation look like?
a number between 1 and less than 10 x a power of 10
3.2 10
3
6.03 10
15
Rules for converting standard
form to Scientific Notation
1. Move the decimal to the right of the first nonzero number
2. Count the # of places the decimal moved
(that is the exponent on 10)
Original number > 1 then positive exponent on the 10
Original number < 1 then negative exponent on the 10
Let’s work together!
1. 123,000,000,000,000 1.23  10
14
2. 0.000000000236
2.36  1010
You Try!
1. 7,080,000,000,000
2. 0.00000001256
1. 7.08 1012
2. 1.256 108
To convert to standard form
• Move the decimal the number of places
of the power of 10.
– Move to the right for positive exponents
– Move to the left for negative exponents.
1.23  10
8
123, 000, 000
1.23 10
8
0.0000000123
numbers in Scientific Notation
To add or subtract numbers in scientific
notation must have the same power of
10!

1.256 10
8
 
 2.34110
8
  2.34110   1.256 10 
8
Add/Subtract the numbers. Remember to line the decimals
up; the power of 10 will remain the same in your answer.
1.256  10
+
8
2.34110
8
2.341 10 8
1.256  108
3.597  10 8
1.085 108
8
What happens when the
number is greater than 10?
4.28 10  9.627 10
5
4.28 10
+
9.627 10
13.907 10
Make sure that you
scientific notation;
that number must be
at least 1 but less
than 10
5
5
5
1.3907 10
5
6
Remember to change
the power of 10 too.
In Summary. . .
• Scientific notation is used to
Write really big/small numbers easier
_____________________.
• To add or subtract numbers in
scientific notation ______________
The powers of 10 MUST be the same. Line up the decimals,
____________________________.
add/subtract and keep the power of 10.
• After adding or subtracting numbers
in scientific notation you need to
check and make sure that they are in
Scientific Notation
__________
still.
Multiplication with Scientific Notation
4 Simple steps
Step 1: Multiply the numerical portion as normal.
Step 2: Multiply the powers of 10 using the
exponent rules.
number and a power of 10.
Step 4: Check to make sure you don’t have to fix
Ex. :
4.310  2 10 
2
8
• Step 1: Multiply 4.3 and 2
4.3 2  8.6
• Step 2: Multiply 102 and 108
10 2 108  1010
• Step 3: Write the answer in Scientific
Notation.
10
8.6  10
Step 4: Is the answer in Scientific Notation? Yes
Let’s look at another one…
 4.2 10  3.8 10 
12
7
Multiply 4.2 and 3.8 together
 4.23.8  15.96
Multiply the powers of 10 together using
exponent rules
Write in Scientific Notation
10  10
7
12
 10
15.96 10
Is the answer in Scientific Notation?
Rewrite the answer in Scientific Notation
5
5
No
1.596 10
4
Division with Scientific Notation
• The same steps apply with division of scientific
notation.
• Step 1: Divide the numbers first.
• Step 2: Divide the powers of 10 using exponent
rules
a number and a power of 10.
notation.
Examples
• Ex. 1:
7.7 10
7 104
6
• Step 1: Divide the numerical portion.
7 .7
 1 .1
7
• Step 2: Simplify the power of 10 portion using
exponent rules.
6
10
2
 10
4
10
• Step 3: Write in scientific Notation
2
scientific notation.
1.1 10
One more time!
Divide
2.8 10
9
3.2 10
4
First divide 2.8 by 3.2
2.8
 .875
3.2
Now divide the powers of 10 using
exponent rules
104
4 9
5

10

10
109
0.875 105
Write in Scientific Notation
Is this in Scientific Notation? No, it needs fixed!
8.75 10
6
Try these examples
1. 2 10  1.43 10
5
12

2. 3.2 10  3 10 
4
9.6 105
3. 3 109
5 107
4.
3.8 107
6
1. 2.86 x 1017
2. 9.6 x 10-10
3. 3.2 x 10-4
4. 1.31579 x 100
In Summary. . .
• When multiplying numbers in Scientific
Notation
Multiply the numbers as normal and use exponent rules
when multiplying the powers of 10.
______________________________
• When dividing numbers in Scientific
Notation
Divide the numbers as normal and use the exponent
rules to divide the powers of 10
________________________________
```