Download Scientific Notation Notes Work Sheet

Scientific Notation Notes Work Sheet
Physics 1-2
Scientific Notation is used to make long numbers manageable.
Example
4,851,000,000
Step 1 Move the decimal so that only one number (1 to 9) is to the left, between the 4 and 8
(4.8) this is the coefficient. Count the number of the places the decimal is moved. (The
decimal is not written, but is understood to be after the last zero we are going to move it
left between the 4 and the 8.)
we moved it 9 places
Step 2
Write the coefficient with the correct number of significant figures (sig. figs.) times 10 with an
exponent equal to the number of places you moved the decimal point.
Use + exponent if you moved the decimal to the left.
Use – exponent if you moved the decimal to the right.
So 4,851,000,000 with 4 sig. figs. becomes 4.851 x 109 all the extra zeros are gone
Example 2
0.000009349 put into scientific notation with 3 sig. figs.
Step 1. We move the decimal right between the 9 and the 3, and we count 6 places.
Step 2. We round off 9.349 to 9.35 and add x 10-6
So we get 9.35 x 10-6
Now try putting these into scientific notation, with 3 sig. figs. (2 decimal places) round if needed.
Answers on page 3
A. 874,500
B. 1,000,000,000
C. 678,000.000,000,000
D. 0.00000007891
E.0.0005895
F.0.000000006537
Converting a number to standard notation
Do the opposite of above.
Example 5.67 x 104 = ?
• Write the coefficient 5.67
• The move the decimal 4 places to the right (Remember a + exponent makes the number big)
• Moving it 2 places give me 567 to move the remaining two, add zeros.
• We get 56,700
Now try these. Answers on page 3
G. 1.23 x 105
H. 9.91 x 108
I. 2.77 x 103
J. 5.98 x 10-5
K. 8.87 x 10-3
L. 4.32 x 10-9
Multiplying Numbers in Scientific Notation
• multiply the coefficients
• add exponents
• if the answer is greater than 10 move the decimal 1 to the left increase the exponent by 1
• example 3.00 x 105 x 4.00 x 103 =
• 3.00 x 4.00 = 12.00 x 108
• 1.20 x 109
Now try these. Answers on page 3
M. 3.0 x 103 x 2.0 x 104 =
N. 3.0 x 103 x 2.0 x 10-4=
O. 3.0 x 10-3 x 2.0 x 104 =
P. 3.0 x 10-3 x 2.0 x 10-4=
Q. 3.0 x 106 x 4.0 x 107=
R. 7.0 x 10-6 x 8.0 x 10-7=
Dividing Numbers in Scientific Notation
• divide the numbers
• subtract the exponents
• if the answer is a decimal, move the decimal 1 to the right and decrease the exponent by 1
• example 4.00 x 10-6 ÷ 8.00 x 10-8 =
• 4.00 ÷ 8.00 = 0.50 x 102
• 5.00 x 101
Now try these. Answers on page 3
S. 9.0 x 109 ÷ 3.0 x 106 =
T. 9.0 x 109 ÷ 3.0 x 10-6 =
U. 9.0 x 10-9 ÷ 3.0 x 106 =
V. 9.0 x 10-9 ÷ 3.0 x 10-6 =
W. 2.0 x 109 ÷ 6.0 x 106 =
X. 4.0 x 108 ÷ 8.0 x 103 =