Grade 10 Science - Unit 2 Chemistry
Scientific Notation
What is this number?
? 300 000 000 m/s
? 0.000 000 000 753 kg
These numbers are very hard to write. A method has been
developed to express very large or small numbers. The method
is called scientific notation.
Scientific notation is based on powers of the base number 10.
The number 300 000 000 is written as 3.0 X 108
The first number 3 is called the COEFFICIENT. It must be
greater than or equal to 1 and less than 10.
The second number is called the BASE. It must always be 10 in
scientific notation. The base number 10 is always written in
exponent form. In the number 3.0 x 108 the number 8 is referred
to as the exponent or power of ten.
To write a number in scientific notation, a decimal is put after the
first digit and zeroes are dropped.
? The coefficient in the number 123,000,000,000 is 1.23
? To find the exponent count the number of places from the
decimal to the end of the number. There are 11 places In
123,000,000,000.
? Thus, 123,000,000,000 is 1.23 X 1011.
Exponents are often expressed using other notations. The
number 123,000,000,000 can also be written as 1.23E+11 or as
1.23 X 10^11.
Numbers smaller than 1 will have a negative exponent. A
millionth of a second (0.000001) is 1.0E-6 or 1.0^-6 or 1.0 X 10-6
Grade 10 Science – Unit 2 Chemistry
Significant Digits and Scientific Notation
Significant Digits
3560.39
356.0
SD =
SD =
356
SD =
0.0125
SD =
0.01250
SD =
350.2 – 63.45
=
=
26.23 / 1.9
=
=
Scientific Notation
2,700,000
=
0.965
=
260
=
0.16
=
Grade 10 Science – Unit 2 Chemistry
The Metric System (SI)
Rules for SI System of Units
Correct
Incorrect
1. Leave a space between the
number and the unit
75 cm
75cm
2. No periods except at the end
of a sentence
4.5 g
4.5 g.
3. Put numbers and symbols
together
6 kg
six kilograms
6 kilograms
six kg
4. Use decimals, not fractions
1.5 L
1½ L
5. Always put a zero in front of
the decimal for numbers less
than one.
0.0025 cm
.0025 cm
1. Group digits in threes for long
numbers. Do not use
commas.
14 091.205 s
14,901.205 s
2. Do not put “s” after the unit
symbol.
10 kg
ten kilograms
10 kgs
Grade 10 Science – Unit 2 Chemistry
Significant Figures
Identify the number of significant digits in the following examples.
? 0.0000067
? 2001
? 3.60
? 4.3 kg
? 200 393 cm
? 0.005 g
? 0.0050 N
Scientific Notation
Extremely large and small numbers are difficult to record in full. A standardized
reporting format is used called scientific notation.
1.
The distance between Mercury and the Sun is 5.8 X 107 km. It is not
written as 58 000 000 km. What does 107 mean?
2.
What is the effect on the exponent by moving the decimal place in the
following direction?
…to the left __________________________
…to the right _________________________
3.
Rewrite the following measurements in scientific notation.
a)
b)
c)
a)
b)
c)
d)
e)
4.
0.000045 km
90 200 s
0.0076 cm
290 000 N
0.000042 km
20 s
0.0623 W
456 000 000 g
Rewrite the following in full.
a)
b)
c)
d)
e)
0.56 X 10-4
3 X 100
3.4 X 10-3
1.6 X 102
9.4 X 104
Grade 10 Science - Unit 2 Chemistry
Measurement, Conversion and Significant Figures
Unit Conversions
? Time
? Distance
1 h = 60 min, 1 min = 60 s
1 km = 1000 m
Conversion Examples
1. Convert 4 h to seconds
2.
Convert 5.2 km to metres
3.
Convert 25 m/s to km/h
Grade 10 Science – Unit 2 Chemistry
Measurement and Significant Figures
Task - Suggest the best unit to measure each line below, estimate the length of
each line and record these in the table below. Then, carefully measure
each line below and complete the table (use proper significant figures).
1
2
3
4
5
6
Line #
1
2
3
4
5
6
Line 6
width
Text
thickness
Text
page
length
Floor tile
width
Best Unit
Estimated
Length
(L1)
Measured
Length
(L2)
Difference
(L2 – L1)
% Error
= (L2 – L1) / L2 X 100
Grade 10 Science – Unit 2 Chemistry
Significant Digits and Scientific Notation
Answers
Significant Digits
3560.39
356.0
SD = 6
SD = 4
356
SD = 3
0.0125
SD = 3
0.01250
SD = 4
350.2 – 63.45
= 286.75
26.23 / 1.9
= 13.805…
= 286.8
= 14
Scientific Notation
2,700,000
RULE
= 2.7 X 106
0.966
= 9.65 X 10-7
261
= 2.6 X 102
0.17
= 1.6 X 10-2
+ exponential
- exponential
Grade 10 Science - Unit 2 Chemistry
Measurement, Conversion and Significant Figures
Answers
Unit Conversions
? Time 1 h = 60 min, 1 min = 60 s
? Distance
1 km = 1000 m
Conversion Examples
1. Convert 4 h to seconds
1 h = 3600 s (Conversion Factor)
4 h X 3600 s/1 h = 14400 s
2.
Convert 5.2 km to metres
1 km = 1000 m
5.2 km X 1000 m/1 km = 5200 m
3.
Convert 25 m/s to km/h
1000 m = 1 km
3600 s = 1 h
25 m/s X 3600 s/1 h X 1 km/1000 m = 90 km/h
Grade 10 Science – Unit 2 Chemistry
Significant Figures
Answers
Identify the number of significant digits in the following examples.
? 0.0000067 (2)
? 2001
(4)
? 3.60
(3)
? 4.3 kg
(2)
? 200 393 cm (6)
? 0.005 g
(1)
? 0.0050 N
(2)
Scientific Notation
Extremely large and small numbers are difficult to record in full. A standardized
reporting format is used called scientific notation.
The distance between Mercury and the Sun is 5.8 X 107 km. It is not
written as 58 000 000 km. What does 107 mean?
7
(10 refers to 10 to the power of 7 OR 10 X 10 X 10 X 10 X 10 X 10 X 10)
1.
2.
What is the effect on the exponent by moving the decimal place in the
following direction?
…to the left __________________________(exponent is
positive (increases))
…to the right _________________________(exponent is
negative (decreases))
3.
Rewrite the following measurements in scientific notation.
a)
b)
c)
d)
e)
f)
g)
h)
4.
0.000045 km
(4.5 X 10-5)
90 200 s
(9.02 X 104)
0.0076 cm
(7.6 X 10-3)
290 000 N
(2.9 X 105)
0.000042 km
(4.2 X 10-5)
20 s
(2.0 X 101)
0.0623 W
(6.23 X 10-2)
456 000 000 g
(4.56 X 108)
Rewrite the following in full.
a) 0.56 X 10-4
b) 3 X 100
c) 3.4 X 10-3
d) 1.6 X 102
e) 9.4 X 104
(0.00056)
(3)
(0.0034)
(160)
(96 000)