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Scientific Notation PowerPoint PPT Presentation

7.1b  Determine scientific notation for small and big numbers. Scientific Notation. What is Scientific notation?. Use to express very large numbers The distance from the Earth to the Sun 152,000,000 km. What is Scientific notation?. Use to express very Small numbers.

Scientific Notation

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7.1b  Determine scientific notation for small and big numbers.

Scientific Notation

What is Scientific notation?

• Use to express very

• large numbers

• The distance from

• the Earth to the Sun

• 152,000,000 km

What is Scientific notation?

• Use to express very Small numbers.

• The size of a hemoglobin cell

• 0.0000000065 m

How do you write a number in scientific notation?

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:

• 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:

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:

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

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

• 9872432

• 0.0000345

• 0.08376

• 5673

9.872432 x 106

3.45 x 10-5

8.376 x 10⁻2

5.673 x 103

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,