learning goals: 1. state whether or not a number is in scientific notation….and why. 2. write a...

Learning Goals:1. State whether or not a number is in

Scientific Notation….and why.2. Write a given number in Scientific

Notation.

Scientific Notation!

What does it mean??

Scientific Notation!

Do you know this number?

300,000,000 m/sec.

It's the speed of light !

(The speed at which light

travels.)

Do you know this number?

120,000 km

It's the diameter of

Saturn!

Scientists have developed a shorter method

to express very large or very small numbers.

This method is called scientific notation.

Scientific Notation is made of two factors:

A coefficient and a power of 10.

_____ x 10

Let’s look at some

examples!

What do all of the Scientific Notation

representations have in common?

Standard Notation

Scientific Notation

123,000,000,000 1.23 x 1011

56,000,000 5.6 x 107

387,000,000 3.87 x 108

7,000 7.0 x 103

Discuss with a partner and share out.

What do all of the coefficients

have in common?

1.23 x 1011

5.6 x 107

3.87 x 108

7.0 x 103

Discuss with a partner and share out.

What do all of the powers of 10

have in common?Discuss with a partner and share out.

1.23 x 1011

5.6 x 107

3.87 x 108

7.0 x 103

What do all of the exponents represent?

Discuss with a partner and share out.

123,000,000,000 1.23 x 1011

56,000,000 5.6 x 107

387,000,000 3.87 x 108

7,000 7.0 x 103

The number 132,400,000,000 in scientific notation is written as which of the following:

1.324 x 1011

13.24 x 1010OR

The number 89,000,000 in scientific notation is written as which of the

following:

8.9 x 106

OR8.9 x 107

The number 3,875 in scientific notation is written as which of

the following:

3.875 x 100

OR3.875 x 103

Write the number 76,000 in scientific notation:

Let’s take a look at some very

small numbers!

Do you recognize this number?

0.000000000753 kg.

It is the mass of a single dust particle!

Do you recognize this number?

0.000017 m

It is the width of a

single human hair!

Let’s look at some

examples!

What do all of the Scientific Notation

representations have in common?

Standard Notation Scientific Notation

0.000000078 7.8 x 10-8

0.0000456 4.56 x 10-5

0.0000000094 9.4 x 10-9

0.0007 7.0 x 10-4

Discuss with a partner and share out.

What do all of the coefficients

have in common?Discuss with a partner and share out.

7.8 x 10-8

4.56 x 10-5

9.4 x 10-9

7.0 x 10-4

What do all of the powers of 10

have in common?Discuss with a partner and share out.

7.8 x 10-8

4.56 x 10-5

9.4 x 10-9

7.0 x 10-4

What do all of the exponentsrepresent?

Discuss with a partner and share out.

0.000000078 7.8 x 10-8

0.0000456 4.56 x 10-5

0.0000000094 9.4 x 10-9

0.0007 7.0 x 10-4

The number 0.000000049 in scientific notation is written as which of the following:

49 x 10-8

OR4.9 x 10-8

The number 0.00003 in scientific notation is written as which of the

following:

3 x 10-5

OR0.3 x 10-4

The number 0.00000000707 in scientific notation is written as

which of the following:

7.7 x 10-10

OR7.07 x 10-9

Write the number 0.0000065 in scientific

notation:

Sarah vs. Stacy 

There’s a correct way to write Scientific Notation, just like the Order of Operations. Without a set standard,

several answers could actually be correct.

Using the standards you just learned, decide which student is correctly

writing the numbers.

Sarah vs. StacyProblem #1

831,000Sarah thinks the answer is

Stacy thinks the answer is

8.31 X 105 8.31 X 10-5

Who is correct? And how do you know?

What mistake did the incorrect student make?

Sarah vs. StacyProblem #2

0.00345Sarah thinks the answer is

Stacy thinks the answer is

3.45 X 10-2 3.45 X 10-3

Who is correct? And how do you know?

What mistake did the incorrect student make?

Sarah vs. StacyProblem #3

0.0000006Sarah thinks the answer is

Stacy thinks the answer is

0.6 X 106 6.0 X 10-7

Who is correct? And how do you know?

What mistake did the incorrect student make?

On Your Own!!A.

8.24 x 3-5B.

9.71 x 108

C.

0.4 x 102D.

39.13 x 10-4

1. Which number below is written in Scientific Notation?

2. Write the following numbers in Scientific Notation:480,000 0.000734