SCIENTIFIC NOTATION
A value written as the product of two numbers: a
coefficient and 10 raised to a power.
Ex: 602,000,000,000,000,000,000,000
is 6.02 × 1023
The coefficient in this number is 6.02.
(It is always a number equal to or greater than 1,
and less than 10.)
The power of 10, or exponent, is 23.
Entering scientific notation correctly in a calculator is
important.
Here is the procedure for our classroom calculators:
6.02 × 1023 is entered as
6 . 0 2 EE 23
Some calculators may require you to press “2nd EE”,
or EXP instead of EE
Calculations with Scientific Notation:
Adding: convert all numbers to the same power of 10,
then add coefficients.
6.02 X 1023 + 3.01 x 1024 =
0.602 x 10 24 + 3.01 x 10 24 = 3.61 x 10 24
Subtracting: convert all numbers to the same power of
10, then subtract coefficients.
6.02 X 1024 - 3.01 x 1023 =
6.02 x 10 24 - 0.301 x 10 24 = 5.72 x 10 24
Calculations with Scientific Notation:
Multiplying: multiply coefficients and add exponents.
6.02 X 1023
x
3.01 x 1024 = 18.1 x 10 47
Dividing: divide coefficients and subtract exponents.
6.02 X 1024
÷ 3.01 x 1023 = 2.00 x 101
SIGNIFICANT FIGURES
• What are they good for?
– They tell us how precise a measurement is.
The more significant figures, the more
precise the measurement.
• How do you know how many you have?
– All known digits that you can read from the
ruler, graduated cylinder, etc, plus one
estimated digit.
When is a digit significant?
(red ones ARE)
1. Every nonzero digit is significant.
24.7 m, 0.743 m, and 714 m
2. Zeros between nonzero digits are significant. 7003 m, 40.79 m
3. Leftmost zeros appearing in front of nonzero digits are not significant.
They are placeholders.
0.000099 meter
4. Zeros at the end and to the right of a decimal point are significant
43.00 m, 1.010 m , 9.000 m
5. Zeros at the rightmost end, left of an understood decimal point are not
significant if they serve as placeholders.
300 m, 7000 m, and 27,210 m
(If they ARE known measured values, however, then they would be
significant. Writing the value 300m in scientific notation as 3.00 x 102 m
makes it clear that these zeros are significant.)
6. Counting values & exactly defined quantities have an unlimited number
of significant figures;. 23 students, 60 min = 1 hr
When calculating with measurements, how do you know
the correct number of significant figures for your answer?
An answer cannot be more precise than the least
precise measurement from which it was calculated.
The answer must be rounded to make it consistent
with the measurements from which it was
calculated.
Density = mass/volume 11.2 g / 2.1 ml = 5.333333333333333 g/ml
= 5.3 g/ml
How do you round the answers?
Once you know the number of significant figures your
answer should have, round to that many digits, counting
from the left.
* If the digit immediately to the right of the last
significant digit is less than 5, drop it and the last
significant digit stays the same.
* If the digit in question is 5 or greater, the last significant
digit is increased by 1.
Adding / Subtracting measurements:
The answer to an addition or subtraction
calculation should be rounded to the
same number of decimal places (not
digits) as the measurement with the least
number of decimal places.
12.52 meters
349.0 meters
+ 8.24 meters
369.76 meters
369.8 meters
Multiplication and Division
Round the answer to the same number of
significant figures as the measurement with
the least number of significant figures.
7.55 m x 0.34 m = 2.567 m2
= 2.6 m2
(0.34 meter has the least number of significant figures: two.)
prefix
symbol
value
expanded value
yotta
Y
1024
1 000 000 000 000 000 000 000 000 U.S. septillion; U.K. quadrillion
zetta
Z
1021
exa
E
1018
peta
P
1015
tera
T
1012
giga
G
109
1 000 000 000 U.S. billion
mega
M
106
1 000 000 million
kilo
k
103
1 000 thousand
hecto
h
102
100 hundred
deca
da
101
100
English name
1 000 000 000 000 000 000 000 U.S. sextillion
1 000 000 000 000 000 000 U.S. quintillion; U.K. trillion
1 000 000 000 000 000 U.S. quadrillion
1 000 000 000 000 U.S. trillion; U.K. billion
10 ten
1
one
deci
d
10-1
0.1
tenth
centi
c
10-2
0.01
hundredth
milli
m
10-3
0.001
thousandth
micro u
10-6
0.000 001
millionth
nano
n
10-9
0.000 000 001
U.S. billionth
pico
p
10-12
0.000 000 000 001
U.S. trillionth; U.K. billionth
femt
o
f
10-15
0.000 000 000 000 001
U.S. quadrillionth
atto
a
10-18
0.000 000 000 000 000 001
U.S. quintillionth; U.K. trillionth
zepto
z
10-21
0.000 000 000 000 000 000 001
U.S. sextillionth
yocto
y
10-24
0.000 000 000 000 000 000 000
001
U.S. septillionth; U.K.
quadrillionth