Post on 19-Nov-2014
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.