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### Scientific Notation

7.1b Determine scientific notation for small and big numbers.

What is Scientific notation? numbers.

- Use to express very
- large numbers
- The distance from
- the Earth to the Sun
- 152,000,000 km

What is Scientific notation? numbers.

- Use to express very Small numbers.
- The size of a hemoglobin cell
- 0.0000000065 m

How do you write a number in scientific notation? numbers.

A number written in scientific notation has two parts:

1

10x10x10x10x10

1st part: a number between 1 and 10 1 n < 10

1, 2,3, 4, 5, 6, 7, 8, 9.

2nd part: a power of 10

10⁴ = 10x10x10x10= 10,000

10⁻⁵=

= 0.00001

In Scientific Notation, there are two kinds of exponents: positive and negative

A positive exponent

tells you: The number

is greater than one

Positive Exponent:

2.35 x 104

Negative Exponent:

3.97 x 10

-3

A negative exponent

tells you:The number

is less than one

From scientific notation to standard form, the exponent tells you how you should move the decimal point:

If you have a positive exponent, move the decimal point to the right:

4

10

Positive Exponent:

2.31 x 104

2.31 x10x10x10x10

23.1 x10x10x10

231.x10x10

2310.x 10

23100.

2.31 x 104

2 3 1

=

0

0

From scientific notation to standard form, the exponent tells you how you should move the decimal point:

Negative Exponent: 3.97 x 10-3 =

3.97

10x10x10

0.397

10x10

If you have a Negative exponent, move the decimal point to the Left:

0.0397

10

0

0

0

3 9 7

3.97x 10-3

0.00397

=

An easy way to remember this is: tells you how you should move the decimal point:

- If an exponent is positive:
The number gets larger, so move the decimal to the right.

- If an exponent is negative:
The number gets smaller, so move the decimal to the left.

The exponent also tells how many spaces to move the decimal: tells you how you should move the decimal point:

5 3 5

0

0

In this problem, the exponent is +4, so the decimal moves 4 spaces to the right.

The exponent also tells how many spaces to move the decimal: tells you how you should move the decimal point:

0

0

0

0

4 0 8

10x10x10x10

In this problem, the exponent is -4, so the decimal moves 4 spaces to the left.

Try changing these numbers from Scientific Notation to Standard Notation:

- 9.678 x 104
- 7.4521 x 10⁻3
- 8.513904567 x 107
- 4.09748 x 10-5

96780

0.0074521

85139045.67

0.0000409748

How do you change from Standard Notation to Scientific Notation:

1) First, move the decimal after the first whole number:

3 2 5 8

2) Second, add your multiplication sign and your base (10).

x

3.258

10

3) Third, Count how many spaces the decimal moved and this is the exponent.

3 . 2 5 8 x 10

3

3

2

1

How do you change from Standard Notation to Scientific Notation:

4) See if the original number is greater than or less than one.

- If the number is greater than one, the exponent will bepositive.
348943 = 3.489 x 105

- If the number is less than one, the exponent will be negative.
0.0000000672 = 6.72 x 10-8

Try changing these numbers from Standard Notation to Scientific Notation:

- 9872432
- 0.0000345
- 0.08376
- 5673

9.872432 x 106

3.45 x 10-5

8.376 x 10⁻2

5.673 x 103

Order the following number from least to greatest, use scientific notation form.

a)

3.5x10⁴,

3.5x10⁵,

3.5x10⁻²

3.5x10⁻²,

3.5x10⁴,

3.5x10⁵

b)

5.3x10⁴,

3.5x10⁴,

35.0x10⁴

3.5x10⁴,

5.3x10⁴,

3.5x10⁵

c)

5300,

53000,

0.000053

5.3 x10⁻⁶,

5.3x10³,

5.3x10⁴,

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