SCIENTIFIC NOTATION

You will learn:

•how to express numbers in scientific notation

•how to express numbers in standard form

SCIENTIFIC NOTATION

WARM UP 1. Simplify:

2.3k – 5 = 7k – 21

3.(

4.Find the sum of the integers between and

5. x

Directions:

With your partner, fix the following text message that you need to send to me. It is too long to send.

“Hello Ms Jones, please help! I don’t know what time school starts tomorrow, thanks!”

SCIENTIFIC NOTATIONWhen dealing with very large or very small numbers, keeping track of place value can be difficult. For this reason, numbers such as these are often expressed in scientific notation.

A number is expressed in scientific notation when it is written as a product of a factor and a power of 10. The factor must be greater than or equal to 1 and less than 10.

A number in scientific notation is written as where 1 ≤ a < 10 and n is an integer.

https://www.youtube.com/watch?v=Dme-G4rc6NI

Use these steps to express a number of the form in standard notation.

1.Determine whether n>0, or n<0.2.If n>0, move the decimal point in a to the right n

places.3.If n<0, move the decimal point in a to the left n places.4.Add zeros, decimal point, and/or commas as needed to

indicate place value.

Examples:a.2.45 x = 2.45 x 100,000,000 = 245,000,000 (n = 8 so

move the decimal point 8 times to the right)b.3 x = 3 x = 0.00003 (n = -5 so move the decimal

point 5 places to the left.)

Scientific to standard notation

You try these……….

1.3.45 x

2.4.6 x

STANDARD TO SCIENTIFIC NOTATIONUse these steps to express a number in scientific notation:

1. Move the decimal point so that it is to the right of the first nonzero digit. The result is a decimal number a. 2. Observe the number of places n and the direction in which you moved the decimal point.3. If the decimal point moved to the left, write as 4. If the decimal point moved to the right, write as Examples:

• 30,500,000 → 3.0500000 x (move the decimal point 7 places to the left.) 30,500,000 = 3.05 x (a = 3.05 and n = 7)

• 0.000781 → 00007.81 x (move the decimal point 4 places to the right. 0.000781 = 7.81 x (a = 7.81 and n = -4)

You try these…..

1.45,000,000,000

2.0.000000567

The following information shows chocolate and candy sales during a recent holiday:

Candy Canes: $120 million

Chocolate: $300 million

All candy: $1.45 billion

1.Express the sales of candy canes, chocolates, and all candy in standard notation.

2. Write each of these sales figures in scientific notation.

Using Scientific Notation. . . .

Problems to solve:

1.In the 1930’s the Indian physicist, Subrahmanyan Chandrasekhar and others predicted the existence of neutron stars. These stars can have a density of 10 billion tons per teaspoonful. Express this density in scientific notation.

2. The unit of measure for counting molecules is a mole. One mole of a substance is the amount that contains about 602,214,299,000,000,000,000,000 molecules. Write this number in scientific notation.

CLASSWORK

Complete the worksheet. Attempt to answer each problem on your own. Check your work with your partner.

Did you get today’s lesson? Let’s see. Complete the short ticket out the door.

Practice converting numbers from standard form to scientific notation and from scientific notation to standard from.

Complete the worksheet. If you need help, watch the video clip on slide three.

Rules to Remember!If a number is greater than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation.

positive

left

Copy this slide into your notes.

Rules to Remember!

If a number is less than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation.

negative

right

Copy this slide into your notes.

1. Move the decimal to the right of the first non-zero

number.2. Count how many places the

decimal had to be moved.3. If the decimal had to be moved

to the right, the exponent is negative.

4. If the decimal had to be moved to the left, the exponent is positive.

To write a number in scientific notation:

EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS

PROBLEMS ANSWERS

1) 4.9 X 102

2) 3.75 X 10-2

3) 5.95 X 10-4

4) 9.46 X 103

5) 3.87 X 101

6) 7.10 X 100

7) 8.2 X 10-5

1) 490

2) .0375

3) .000595

4) 9460

5) 38.7

6) 7.10

7) .000082

Write these numbers in scientific notation.

P

1) .000122) 10003) 0.014) 125) 0.9876) 5967) 0.000 000 78) 1,000,0009) 0.00125710) 987,653,000,00011) 8

1) 1.2 x 10-4

2) 1 x 103

3) 1 x 10-2

4) 1.2 x 101

5) 9.87 x 10-1

6) 5.96 x 102

7) 7.0 x 10-7

8) 1.0 x 106

9) 1.26 x 10-3

10) 9.88 x 1011

11) 8 x 100

Problems Answers