Section 1.2

Why use it?  Some numbers are too big or too small to write using regular form (also called standard notation)  Using Scientific Notation often makes it easier to multiply or divide numbers without a calculator  How would you express an answer of L to only 3 significant digits?

What does it look like?  Scientific Notation takes the form Coefficient × 10 exponent Coefficient is always ≥ 1 but < 10. The exponent is either a positive or negative whole number.

What does the exponent tell me?  Exponents less than 0  These are numbers that are smaller than 1  Exponents equal to 0  The number is between 1 and 10.  Exponents greater than 0  The number is greater than 10.

Here’s how to use it:  Take any number, let’s say… 503  To turn it into scientific notation, place a decimal point that results in a number between 1 and 10.  You moved it 2 places to the left. Remember that number. 5.03

And now for the exponent… 5.03 is what you got from the previous step. You moved the decimal point 2 places to the left to get there, so use 2 for your exponent. 5.03× 10 2

One more example  Turn this number into scientific notation:  To turn it into scientific notation, move the decimal place until you get the coefficient!  You moved it 5 places to the right. Remember that number

And now for the exponent… 3.41 is what you got from the previous step. You moved the decimal place 5 places to the right to get there, so use -5 for your exponent. 3.41× 10 -5

Multiplying Scientific Notation  When multiplying two scientific notation numbers together…  MULTIPLY the coefficients  ADD the exponents

Example: Multiply: (3.2 × 10 3 ) × (4.0 × 10 5 )  MULTIPLY the coefficients 3.2 × 4.0 = 12.8  ADD the exponents = 8  The result is… 12.8 × 10 8  Converting to accepted scientific notation… 1.28 × 10 9

Dividing Scientific Notation  When dividing two scientific notation numbers…  DIVIDE the coefficients  SUBTRACT the exponents

Example: Divide: (6.4 × 10 3 ) ÷ (2.0 × 10 5 )  DIVIDE the coefficients 6.4 ÷ 2.0 = 3.2  SUBTRACT the exponents = -2  The result is… 3.2 × 10 -2

Scientific Notation and significant digits  6.23 x 10 2 K has how many sigfigs?  x m?  How would you express an answer of L to 3 significant digits?  5.00 x 10 4 L (this cannot be done using standard notation)

Useful exponents to memorize 110 -9 nano-(billionth) 110 -6 micro-(millionth) 110 -3 milli-(thousandth) 110 -2 centi-(hundredth) BBase 110 3 kilo-(thousands) 110 6 mega-(millions) 110 9 giga-(billions)