Download Scientific Notation Notes

NOTES FOR SCIENTIFIC NOTATION
In Science, numbers can range from very large to very small.
IE. Avogadro’s number is 602 213 674 000 000 000 000 000
IE. Mass of electron is 0.000 000 000 000 000 000 000 000 000 000 9109 kg
Because it’s hard to write and read such large or small numbers, scientists use what’s called
SCIENTIFIC NOTATION to shorten it up.
1.0 x 105 = Scientific Notation
10000 = Standard Notation
STEPS for changing numbers into scientific notation
1. Figure out where the original decimal place is.
135.6
0.0992
150000
2. Make a mark to the RIGHT of the first non-zero number going from left to right.
1 35.6
0.09 92
1 50000
3. Count how many places it would take you to move from the original decimal to your new mark.
1 35.6
0.09 92
1 50000
4. Now, write the number that is now to the left of your NEW decimal. Then take only the first number
to the right of the NEW decimal and write it down. If the second number to the right of the new decimal
is 5 – 9, you must round the number to the right of the new decimal.
1.4
5. Write x 10
9.9
1.5
after each new number you have written.
1.4 x 10
9.9 x 10
1.5 x 10
6. However many places it took to move the decimal from the original spot to the new spot will be your
exponent to the upper right of the 10.
1.4 x 10 2
9.9 x 10 2
1.5 x 10 5
7. Lastly, if you moved the decimal to the left (so your original number was larger than 0), your
exponent will be positive.
If you moved the decimal to the right (so your original number was smaller than 0), your exponent will
be negative.
1.4 x 10 2
9.9 x 10 -2
1.5 x 10 5
STEPSfor changing numbers into standard notation
1. Check to see if the exponent is positive or negative.
6.7 x 10 -4
8.1 x 10 2
3.0 x 10 -6
2. Find where the decimal is. If the exponent was negative, you will move the decimal to the left (the
final number will be less than 0).
If the exponent is positive, you will move the decimal to the right (the final number will be larger than
0).
6.7 x 10 -4
8.1 x 10 2
3.0 x 10 -6
3. You will move the decimal in the correct direction (from step 2) the number of places that the
exponent tells you. If the exponent is 5, move 5 places, etc. If you run out of numbers, use zeros to fill
in the rest.
0.00067
810
0.0000030
RULES FOR ADDING/SUBTRACTING SCIENTIFIC NOTATION
1. If order to add or subtract, the exponents must be the same number with the same positive or negative
sign. If they are not, you may change one of the numbers.
It may be easiest to change one number from scientific notation to standard. Then after that, rewrite it
so that it is in a different scientific notation.
6.3 x 10 4 
+2.1 x 10 5

63000 
0.63 x 10 5
+2.1 x 10 5
2.73 x 10 5
Do NOT add the exponents, only the numbers.
RULES FOR MULTIPLYING SCIENTIFIC NOTATION
1. First thing, multiply the actual numbers (not the exponents)
( 4.5 x 10 8) x ( 3.2 x 10 5)  4.5 x 3.2 = 14.4
2. Then, add together the coefficients.
10 8 + 10 5  8 + 5 = 13
3. After that, write the new number out.
14.4 x 10 13
RULES FOR DIVIDING SCIENTIFIC NOTATION
1. First thing, divide the actual numbers (not the exponents)
( 6.85 x 10 7) / ( 2.0 x 10 3)  6.85 / 2.0 = 3.425
2. Then, subtract the bottom (or second) exponent from the top (or first)
10 7 – 10 3  7-3 = 4
3. After that, write the new number out
3.425 x 10 4