Scientific Notation Study Guide
Lessons 1.6 & 1.7
Lesson 1.6 : Scientific Notation
Scientific notation is a way to write really large numbers in a
smaller way. It uses powers of ten!
Ex: 3,400,000
3.4 x 106
Number
P of ten
To write in scientific notation:
1)
2)
3)
Put a decimal point between the first two nonzero digits
Count the number of times you moved the decimal
Write the number of moves as a power of ten (the exponent)
*If you start with a WHOLE NUMBER and move to the LEFT exponent is positive
*If you start with a DECIMAL NUMBER and move to the RIGHT exponent is negative
Writing Numbers in Scientific Notation
1)
75,000,000 = 7.5 x 107
2)
6,040,000,000 = 6.04 x 109
3)
.00157 = 1.57 x 10-3
4)
.00000208 = 2.08 x 10-6
Writing Numbers in Standard Form
1)
3.16 x 103 = 3,160
2)
1.1 x 10-4 = 0.00011
3)
2.52 x 10-5 = 0.0000252
4)
9.931 x 105 = 993,100
Scientific Notation Word Problem
The table shows the mass in grams of one atom of each of several elements. List the
elements in order from the least mass to greatest mass per atom.
SOLUTION:
To order numbers when they are in scientific notation, first look for the least exponent or exponents
and then compare the decimal factors.
The mass per atom of hydrogen is the least because the exponent of –24 is the least. Then, since carbon
and oxygen both have an exponent of –23, compare 1.995 and 2.548. Since 1.995 < 2.548, the mass of an
atom of carbon is less than the mass of an atom of oxygen. Lastly, because gold and silver both have an
exponent of –22, compare 3.272 and 1.792. Since 1.792 < 3.272, the mass of an atom of silver is less than
the mass of an atom of gold.
The elements in order from least to greatest mass per atom are hydrogen, carbon, oxygen, silver, and
gold.
Lesson 1.7 : Computing with Scientific Notation
Multiplying and Dividing with Scientific Notation
Example: (2.1 x 104) (1.6 x 105)
Step 1  Multiply the front numbers 2.1 x 1.6 = 3.36
Step 2  Use Law #1 to combine powers of ten 104+5 = 9 = 109
Step 3  Check and Adjust IF NEEDED ….in this case you DON’T
need to because the first number is >1 and <10!
3.36 x 109
Example: (7.2 x 103) (1.6 x 104)
Step 1  7.2 x 1.6 = 11.52
Step 2  103+4 = 7 = 107
Step 3  Check and Adjust IF NEEDED ….in this case you DO need to
because the first number is greater than 10….so 11.52 needs to be
adjusted to 1.152….since we moved the decimal once to the left we also
need to ADD ONE to the exponent 107+1 = 108
1.152 x 108
Example: (6.3 x 10-4) (2.6 x 10-4)
Step 1  6.3 x 2.6 = 16.38
Step 2  10 -4+-4 = -8 = 10-8
Step 3  Check and Adjust 16.38 becomes 1.638 but BE CAREFUL
WHEN YOU ADD ONE TO A NEGATIVE EXPONENT 10-8+1 = 10-7
1.638 x 10-7
Example: 8.37 x 108
2.7 x 103
Step 1  Divide the front numbers 8.37 / 2.7 = 3.1
Step 2  Use Law #2 to combine powers of ten 108-3 = 5 = 105
Step 3  Check and Adjust IF NEEDED ….in this case you DON’T
need to
3.1 x 105
Example: 1.14 x 106
4.8 x 10-6
Step 1  1.14 / 4.8 = 0.2375
Step 2  Use Law #2 to combine powers of ten 106-(-6) = 12 = 1012
Step 3  Check and Adjust IF NEEDED ….in this case you DO need to
because 0.2375 is <1….so .2375 needs to be adjusted to 2.375 and since
we moved the decimal once to the right we also need to SUBTRACT
ONE to the exponent 1012-1 = 1011
2.375 x 1011
** THE ADJUSTING RULE! **
If a number needs to be adjusted and it is….
a # that is LESS THAN 1  SUBTRACT one from the exponent (you
took care of one “move” when you adjusted)
a # that is GREATER THAN 10  ADD one to the exponent (you need
to increase the number of moves for the decimal by 1)
Adding and Subtracting with Scientific Notation
Example: (6.89 x 104) + (9.24 x 105)
Step 1  Adjust FIRST …change the smaller power of ten to the greater
exponent … so 6.89 x 104 becomes .689 x 105
(.689 x 105) + (9.24 x 105)
Step 2  Add/Subtract your front numbers .689 + 9.24 = 9.929
Step 3  Rewrite and Keep the Power of Ten (Check and Adjust IF
NEEDED)
9.929 x 105
Example: (7.83 x 108) – 11,610,000
**Rewrite 111,610,00 in Sci. Not = 1.161 x 107
(7.83 x 108) – (1.161 x 107)
Step 1  1.161 x 107 becomes .1161 x 108
(.7.83 x 108) + (.1161 x 108)
Step 2  7.83 - .1161 = 7.7139
Step 3  Rewrite 7.7139 x 108
7.7139 x 108
PRACTICE PROBLEMS FOR QUIZ
Textbook pg 57 #16-24 (Lesson 1.6)
Textbook pg 65 #17-24 (Lesson 1.7)
See Miss Molinari or Mrs. Labato before or after school for extra help and
review!