Transcript File scientific notation and units of measurement

Scientific Notation
and Units of
Measurement
Scientific Notation

Scientists often deal with both very
large and very small numbers.
Ex. 0.00000000000000001 or 100,000,000,000,000,000

To keep things simple, we express
these numbers as powers of 10.
Scientific Notation
Scientific Notation (cont.)

Scientific notation is expressed as:
M x 10ª
Any number between 1 & 10
Power of 10
“a” determines the
number of powers
Scientific Notation (cont.)
Decimal behind # = right to left = positive
10 power
Example 1.
2500000 0= 2.5 x 106
Decimal in front of # = left to Right =
negative 10 power
Example 2.
000005 = 5 x 10-5
Scientific Notation (cont.)
Class Practice:
1. Convert 31,000 to scientific notation.
3.1 x 104
2.Convert 0.00012 to scientific notation.
1.2 x 10-4
Scientific Notation (cont.)

You can also convert scientific
notation back to standard notation.
Just move the decimal back in the opposite direction
Example 1.
1.4 x 105 = 140,000
Example 2.
1.5 x 10-4 = 0.00015
Scientific Notation (cont.)

Multiplying numbers in scientific
notation:
(4.4 x 106) x (3.9 x 104) = 1.716 x 1011
4.4 x 3.9 = 17.16
6 + 4 = 10
Scientific Notation (cont.)

Dividing numbers in scientific notation:
(5.76 x 109) ÷ (3.2 x 103) = 1.8 x 106
5.76 ÷ 3.2 = 1.8
9–3= 6
Units of Measurement

2 systems of measurement in use
English ( yards, gallons, miles, feet)
Scientists use
this system!!!
Metric (meters, liters, kilometers)
Units of Measurement
(cont.)

Why is it important that we know
what system we are using?
STOP
SPLAT
NASA orbiter (1999): 125 million dollar
conversion error!!!
MARS
Units of Measurement
(cont.)
kilo
hecto
deca
(k)
(h)
(da)
103
102
101
g
L
m
deci
centi
milli
(d)
(c)
(m)
10-2
10-3
10-1
100
Ex 1.
250 g = 0.250 kg
2.5 x 10-1 kg
Ex 2.
250 L = 250,000 mL
2.5 x 105 mL
Ex 3.
250 hg = 25,000,000 mg
2.5 x 107 mg