Scientific Notation

Prepared by: Jirah Zabaljauregui, Sherina Oya, Bryan Yap, Kimberly Lopez, Jasmine Bejino, Justina Holgado, Leinard Casupang, Shiela Mae Aguilar, Clerk Enrado II – Venus

Submitted to: Mr. Delos Santos

What is scientific Notation?

• Scientific notation is a way of expressing really big numbers or really small numbers.

• It is most often used in “scientific” calculations where the analysis must be very precise.

Why use scientific notation?

• For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form.

• Numbers expressed in scientific notation can be used in a computation with far greater ease.

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

Positive Exponent:2.35 x 108

Negative Exponent:3.97 x 10-7

When changing scientific notation to standard notation, the exponent tells you if you should move the decimal:

With a positive exponent, move the decimal to the right:

4.08 x 103 = 4 0 8

Don’t forget to fill in your zeroes!

When changing scientific notation to standard notation, the exponent tells you if you should move the decimal:

With a negative exponent, move the decimal to the left:4.08 x 10-3 = 4 0 8

Don’t forget to fill in your zeroes!

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:

4.08 x 103 = 4 0 8 In this problem, the exponent is +3, so the decimal moves 3 spaces to the right.

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

4.08 x 10-3 = 4 0 8

In this problem, the exponent is -3, so the decimal moves 3 spaces to the left.

Example 1

• Given: 5.093 x 106

• Answer: 5,093,000 (moved 6 places to the right)

Example 2

• Given: 1.976 x 10-4

• Answer: 0.0001976 (moved 4 places to the left)

Practice: Try changing these numbers from Scientific Notation to Standard Notation:

1) 9.678 x 104

2) 7.4521 x 10-3

3) 8.513904567 x 107

4) 4.09748 x 10-5

96780

.0074521

85139045.67

.0000409748

When changing from Standard Notation to Scientific Notation:

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

3 2 5 8

123

3

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

3 . 2 5 8 x 10

3) Count how many spaces the decimal moved and this is the exponent. 3 . 2 5 8 x 10

When changing 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 be positive.

348943 = 3.489 x 105

– If the number is less than one, the exponent will be negative.

.0000000672 = 6.72 x 10-8

Example 1

• Given: 289,800,000• Use: 2.898 (moved 8 places)• Answer: 2.898 x 108

Example 2

• Given: 0.000567• Use: 5.67 (moved 4 places)• Answer: 5.67 x 10-4

Practice: Try changing these numbers from Standard Notation to Scientific Notation:

1) 9872432

2) .0000345

3) .08376

4) 5673

9.872432 x 106

3.45 x 10-5

8.376 x 102

5.673 x 103

Multiplying and Dividing Numbers in Scientific Notation

• The main reason scientists use Scientific notation is because it makes calculations easier

• You never have to multiply or divide by a number larger than 10

• The rest is simply addition or subtraction

Multiplying Numbers in Scientific Notation• Given the following:

– 3x105 ● 5x106 = ?• First step: Operate on the numbers in front

– 3 • 5 = 15• Second step: Operate on the exponents

– When we multiply numbers with exponents, we add the exponents

– 105 ● 106 = 1011 • Third step: put them together

– 15x1011

• Fourth step: check to see if number is in good scientific notation– 15 is bigger than 10– Shift the decimal 1 place and add 1 to exponent– 1.5x1012

Dividing Numbers in Scientific Notation• Given the following:

– 3x105 ÷ 5x106 = ?

• First step: Operate on the numbers in front– 3 ÷ 5 = 0.6

• Second step: Operate on the exponents– When we divide numbers with exponents, we subtract the

exponents– 105 ÷ 106 = 10-1

• Third step: put them together– 0.6x10-1

• Fourth step: check to see if number is in good scientific notation– 0.6 is smaller than 1– Shift the decimal 1 place and subtract 1 (or add -1) from

the exponent– 6x10-2

References:

www.google.com/scientific_notationhttp://www.aaamath.com/dec71i-dec2sci.htmlhttp://janus.astro.umd.edu/cgi-bin/astro/scinote.plhttp://www.sciencejoywagon.com/physicszone/lesson/00genral/dectosci.htm

END OF PRESENATION.