Scientific Notation and Standard Form
Standard Form is how we normally write numbers.
Scientific Notation is a way of writing numbers that are too large and too small to be easily written in standard form. Scientific Notation is a number written in the form Where a is between 1 and 10 and n is an integer.
If the number written in standard form is
__________________________________________________________________________________________________ Let's look at a couple of examples.
The width of the universe is 210,000,000,000,000,000,000,000 miles! (standard form) Let's write this number in Scientific Notation. Where is the decimal?? If a decimal is not shown there is an implied decimal after the last number. Let's continue writing this number in Scientific Notation. STEP 1: Move the decimal so that the number is between 1 and 10. STEP 2: Count how many places the decimal point moved (this determines the exponent). In our example the exponent will be 23.
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Let's try another example, except let's write a very small number in Scientific Notation. Express 0.0000000902 in Scientific Notation. STEP 1: Move the decimal so that the number is between 1 and 10. Notice how the decimal moves behind the first number that is not a zero!
STEP 2: Count how many places the decimal point moved. The exponent will be -8. ___________________________________________________________________________________
Sometimes we will need to convert numbers from Scientific Notation to Standard Form. The exponent tells us how many places to move the decimal. The SIGN of the exponents tells us which direction to move the decimal to make the number large or small. When in Scientific Notation, if the EXPONENT is
____________________________________________________________________________________ Let's look at a couple of Examples. Step 1: Look to see is the exponent is positive or negative.
Step 2: Move the decimal and drop the power of 10. Standard Form is 6,354,000 ____________________________________________________________________________ Step 1: Look to see is the exponent is positive or negative.
Step 2: Move the decimal and drop the power of 10. Standard Form is .000159 |
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