Scientific Notation

Scientific Notation

OBJECTIVE: convert number to scientific notation and to standard form.

Multiple Choice

WARM UP: Which shows (2x²)³ in a simplified form?

• 6x⁵

• 8x⁶

• 6x⁶

• 8x⁵

Scientist have a challenge

They encounter really BIG numbers like...

300,000,000,000,000,000,000,000,000,000,000 kg

or

They encounter really SMALL numbers like...

0.000000000000000000000000030 kg

Standard Notation

Both of these examples

300,000,000,000,000,000,000,000,000,000,000 kg

and

0.000000000000000000000000030 kg

are written in Standard Notation

(it's the way we write numbers all the time)

Scientific Notation

So they come up with a more convenient way to write really BIG numbers or really small numbers.

It's called Scientific Notation.

Scientific Notation DOES NOT change the value of the number. Just makes it easier to write.

Scientific Notation

Scientific Notation uses Powers of 10.

Have a base of 10 and an exponent

Examples:

10¹ = 10 

10² = 10 x 10 = 100

10³ = 10 x 10 x 10 = 1,000

10⁴ = 10 x 10 x 10 x 10 = 10,000

10⁵ = 10 x 10 x 10 x 10 x 10 = 100,000

Multiple Choice

10⁷ is equivalent to...?

• 10,000,000

• 1,000,000

• 100,000,000

• 100,000

Scientific Notation

ALWAYS in a specific form

#.# x 10^#

Example: 2.3 x 10¹²

Scientific Notation to Standard Notation

Video to help you if you are walking through this lesson on your own.

Scientific Notation to Standard Notation

6.5 X 10⁶ = 6.5 x 1,000,000 = 6,500,000

SHORTCUT: if the exponent is positive, move the decimal that many places to the right.

6.5 X 10⁶

the 6 is positive to six places to the right.

Multiple Choice

7.3 x 10⁵ =

• 730,000

• 73,000

• 7,300,000

Multiple Choice

9.2 x 10⁶

• 92,000,000

• 9,200,000

• 920,000,000

• 920,000

Scientific Notation to Standard Notation

Multiple Choice

1.2 x 10^-5

• 0.000012

• 0.0000012

• 0.00000012

• 0.00012

Multiple Choice

4.4 x 10^-5

• 0.0000044

• 0.00000044

• 0.000044

• 0.00044

Standard Notation to Scientific Notation

Video to help you if you are walking through this lesson on your own.

Standard Notation to Scientific Notation

The example is a BIG number.

What I would add is...

Since its a BIG number, my exponent will be positive.

Multiple Choice

Express 9,300,000 in scientific notation.

• 9.3 x 10⁶

• 9.3 x 10⁵

• 9.3 x 10⁷

• 9.3 x 10⁸

Multiple Choice

Express 120,000,000 in scientific notation.

• 1.2 x 10⁷

• 1.2 x 10⁶

• 1.2 x 10⁸

• 1.2 x 10⁹

Standard Notation to Scientific Notation

The example is a SMALL number.

What I would add is...

Since its a SMALL number, my exponent will be negative.

Multiple Choice

Express 0.000037 in scientific notation.

• 3.7 x 10^-5

• 3.7 x 10^-4

• 3.7 x 10^-6

• 3.7 x 10^-7

Multiple Choice

Express 0.000000029 in scientific notation.

• 2.9 x 10^-7

• 2.9 x 10⁸

• 2.9 x 10^-6

• 2.9 x 10^-8

• 2.9 x 10⁶