# 11 Convert 0.00000000578 to scientific notation. 0 . 0 0 0 0 0 0 0 0 5 ```Created by: Aramik Yousefian
Presented by : Lilit Haroyan
LAMC SSC Title V HSI
Length
Relations of U.S. and Metric Units
• 1 in = 2.54 cm (exact)
• 1 yd = 0.9144 m (exact)
• 1 mi = 1.609 km
Relations in U.S. units
• 1 mi = 5280 ft
• 1 mi = 1760 yd
• 1 ft = 12 in
So, 3 ft = 0.9144 m
Mass
Kilogram
kg
Relations of U.S. and Metric units
• 1 lb = 0.4536 kg
• 1 oz = 28.35 g
Relations in U.S. units
• 1 lb = 16 oz
More Conversion Examples
A cooler has a capacity
of 5500 ml.
What is the capacity in
Liters?
Ethyl alcohol has
density of 0.79 g/ml.
What is the volume in
ml of 1.5kg of alcohol?
1L
5500 ml x
1000ml
1000 g
1.5 kg x
1 ml
x
1 kg
1.2 L gas x
= 1900 ml
0.79 g
1000 ml
How many ml of olive
oil (d=0.92g/ml)
weigh the same as
1.2L of gasoline
(d=0.66g/ml)
= 5.5 L
0.66 g
= 792 g gas
x
1L
1 ml
mass of olive oil = mass of gasoline = 792 g
1 ml
792 g oil x
= 860 ml
0.92 g
Put the decimal after the first digit.
After the decimal place,
there are 11 places left
So, we drop the zeros and
write…
1.23 x 10
11
Write 0.0000000000436 in scientific notation.
0.0000000000436
1
2
3
4
5
6
7
8
9 10 11
4.36 &times; 10–11
Convert 0.00000000578 to scientific notation.
0.00000000578
1
2
3
4
5
6
7
8
9
5.78 &times; 10–9
Ordinary Decimal Notation
Scientific Notation
4000
5,720,000,000
–0.00036
0.00036
–36,000
4 x 103
5.72 x 109
–3.6 &times; 10–4
3.6 &times; 10–4
–3.6 &times; 104
• All non-zero digits are always significant.
123456789
• All zeros between two significant digits are always significant.
120450098014
• All zeros before the first non-zero digit are never significant.
0005520481004
• All zeros after the last non-zero digit and after the decimal are always
significant.
1 2 0 0 0 0.
52.0000
• Trailing zeros before the decimal are ambiguous and therefore assumed
to not be significant.
0055.00
0.0043
0.0035
2 sig figs
0.0035
0022005.0
6 sig figs
0022005.0
568000
3 sig figs 568000
0.003010
4 sig figs
0.003010
0,1,2,3 and 4 are always rounded down
5,6,7,8 and 9 are always rounded up
Rounding Decimals
3.1416 rounded to hundredths is 3.14
1.2635 rounded to tenths is 1.3
1.2635 rounded to 3 decimal places is 1.264
Rounding whole Numbers
134.9 rounded to tens is 130
12,690 rounded to thousands is 13,000
1.239 rounded to units is 1
Significant digit calculations
multiplication and division
When multiplying or dividing numbers, the answer
must contain the same number of significant figures
as the measurement with the lowest number of
significant figures.
(1.353) x (0.12) = 1.6
must contain the same number of decimal places as
the measurement with the lowest number of decimal
places.
(15.12) + (5.8) = 20.9
More Calculations
6.48 x 0.22 = 1.4256
1.4
0.006 + 5.24 = 5.246
5.25
8.06
= 2.7793103
2.8
2.9
(3.5) (4.544)
=
5
3.1808
3
Percentage %
77
96
= 77%
100
= 96%
100
What is 35% of 68?
X
35
100X
X = 24
100
24 is 35% of 68.
=
=
68
(68)(35)
100
100
15 is what percentage of 80?
15
X
80X
=
80
(15)(100)
X = 19
80
19% of 80 is 15.
=
100
80
% error =
X 100
accepted value
Also written as
experimental value - theoretical value
% error =
X 100
theoretical value
% Error Example
A student measures the volume of a 1.50 liter
container to be 1.67 liters. What is the percent
error in the student's measurement?
Experimental Value:
Theoretical value:
1.50 L
1.67 L
1.50 - 1.67
% error =
X
1.67
- 0.17
X
1.67
100 =
100
10% error
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