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.

Warm upWarm up1. If you invest $1,000 at 7% for 2 years. How much 1. If you invest $1,000 at 7% for 2 years. How much will you have after two years if it compounds will you have after two years if it compounds annually?annually?

$1144.90$1144.90

2. 2. How much money should I save in an account paying How much money should I save in an account paying 10% interest compounded yearly if I want to have $484 in 10% interest compounded yearly if I want to have $484 in 2 years?2 years?

$400$400

Scientific NotationScientific NotationTSWBAT:• 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 genes in your body.

2) The influenza virus is about 0.00000001 meters in diameter.

What does Scientific What does Scientific Notation look like?Notation look like?

a number between 1 and less than 10 x a power of 10

Original number > 1 then positive exponent on the 10Original number < 1 then negative exponent on the 10

33.2 10 156.03 10

Rules for converting standard form to Scientific Notation1. 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)

Let’s work together!Let’s work together!

1. 123,000,000,000,000 141.23 10

2. 0.000000000236 102.36 10

You Try! You Try! 1. 7,080,000,000,0002. 0.00000001256

1.

2.

127.08 1081.256 10

To convert to standard formTo 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.

81.23 10 81.23 10123,000,000 0.0000000123

Adding and Subtracting Adding and Subtracting numbers in Scientific Notationnumbers in Scientific Notation

To add or subtract numbers in scientific notation must have the same power of 10!

8 81.256 10 2.341 10 Add/Subtract the numbers. Remember to line the decimals up; the power of 10 will remain the same in your answer.

8

8

8

1.256 10

2.341 10

3.597 10

+

8

8

8

2.341 10

1.256 10

1.085 10

8 82.341 10 1.256 10

What happens when the What happens when the number is greater than 10?number is greater than 10?

Make sure that you put your answer into scientific notation; that number must be at least 1 but less than 10

Remember to change the power of 10 too.

5 54.28 10 9.627 10

5

5

5

4.28 10

9.627 10

13.907 10

+

61.3907 10

In Summary. . . In Summary. . . • Scientific notation is used to

_____________________.• To add or subtract numbers in

scientific notation ______________ ____________________________.

• After adding or subtracting numbers in scientific notation you need to check and make sure that they are in __________ still.

Write really big/small numbers easier

The powers of 10 MUST be the same. Line up the decimals, add/subtract and keep the power of 10.

Scientific Notation

Multiplication with Scientific NotationMultiplication 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.

Step 3: Put your answer together as a product of a number and a power of 10.

Step 4: Check to make sure you don’t have to fix the answer.

Ex. :Ex. :• Step 1: Multiply 4.3 and 2 • Step 2: Multiply 102 and 108

• Step 3: Write the answer in Scientific Notation.

82 102103.4

6.823.4 1082 101010

10106.8

Step 4: Is the answer in Scientific Notation? Yes

Let’s look at another one…Let’s look at another one… 7 124.2 10 3.8 10

4.2 3.8 15.96 7 12 510 10 10

515.96 10

No

41.596 10Rewrite the answer in Scientific Notation

Is the answer in Scientific Notation?

Write in Scientific Notation

Multiply 4.2 and 3.8 together Multiply the powers of 10 together using exponent rules

Division with Scientific NotationDivision 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

• Step 3: Put your answer together as a product of a number and a power of 10.

• Step 4: Check that your answer is in scientific notation.

ExamplesExamples• Ex. 1:

• Step 1: Divide the numerical portion.

• Step 2: Simplify the power of 10 portion using exponent rules.

• Step 3: Write in scientific Notation • Step 4: Check to make sure your answer is in

scientific notation.

4

6

107

107.7

1.17

7.7

24

6

1010

10

2101.1

One more time!One more time!Divide

4

9

2.8 10

3.2 10

First divide 2.8 by 3.22.8

.8753.2

Now divide the powers of 10 using exponent rules

44 9 5

9

1010 10

10

Write in Scientific Notation 50.875 10

Is this in Scientific Notation?68.75 10No, it needs fixed!

Your TurnYour TurnTry these examples

1.

2.

3.

4.

125 101.43102

64 103102.3

9

5

103

106.9

7

7

108.3

105

Answers

1. 2.86 x 1017

2. 9.6 x 10-10

3. 3.2 x 10-4

4. 1.31579 x 100

In Summary. . . In Summary. . .

• When multiplying numbers in Scientific Notation

______________________________

• When dividing numbers in Scientific Notation

________________________________

Multiply the numbers as normal and use exponent rules when multiplying the powers of 10.

Divide the numbers as normal and use the exponent rules to divide the powers of 10