SCIENTIFIC NOTATION

AN INFORMATIVE POWERPOINT BROUGHT TO YOU BY LAUREN CALVERT, HALEY DAVIS, AND

DEANNA HEBERT!

SIGNIFICANT FIGURES

• Significant Figures in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated.

• The rules of sig figs are found on page 47.

SCIENTIFIC NOTATION

• A method of writing or displaying numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10

• Example! – The scientific notation of 10,492 is

1.0492 × 104.

ANDDD THIS IS HOW YOU DO IT!

• Changing numbers from scientific notation to standard notation.

• Ex.1  Change 6.03 x 107 to standard notation.

• Remember,  107 = 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10,000,000

• So, 6.03 x 107 = 6.03 x 10,000,000 = 60,300,000

• Answer = 60,300,000

• Instead of finding the value of the base, we can simply move the decimal seven places to the right because the exponent is 7.

• So, 6.03 x 107 = 60,300,000

• Try one with a negative exponent.

• Ex.2 Change 5.3 x 10-4 to standard notation.

• The exponent tells us to move the decimal four places to the left.

• So, 5.3 x 10-4 = 0.00053

CALCULATING WITH SCIENTIFIC NOTATION

• Rule for Multiplication - When you multiply numbers with scientific notation, multiply the coefficients together and add the exponents.  The base will remain 10.

• Rule for Division – When dividing with scientific notation, divide coefficients and subtract the exponents. The base will remain 10.

• Rule for Addition and Subtraction - when adding or subtracting in scientific notation, you must express the numbers as the same power of 10.  This will often involve changing the decimal place of the coefficient.