Unit 1 Numbers

1.1 Units
I will be able to…
• Identify metric and English
units of measurement.
• Explain why scientists use SI
units.
• Measure quantities using
appropriate units for
measurement.

1.1 Units
•Unit – a quantity adopted as a standard
of measurement.
• Measurements must include a quantity
and a unit.
•The two most commonly used units of
measurement are
• English (Imperial) System
• Metric System

1.1 Units
•The English System
• Distance = inch, foot, yard, mile
• Mass = ounce, pound, ton, slug (1 slug = 12 blobs)
• Volume = ounce, cup, pint, quart, gallon
• Time = second, minute, hour, day, year
• Temperature = Fahrenheit
Many English units were based off body
parts of influential people and varied
from region to region.

1.1 Units
•The Metric System
• Distance = cm, m, km
• Mass = gram, kg
• Volume = milliliter, liter
• Time = second, minute, hour, day, year
• Temperature = Celsius
The international prototype kilogram is
made of 90% platinum and 10% iridium.
This mixture of metals is extremely
resistant to environmental factors that
may affect its mass. It is held under very
tight security in St. Cloud, France.

1.1 Units
•Since 1960, scientists worldwide have
used a set of units called the International
System (Le Systeme Internationale in
French) or SI.

1.2 Unit Conversions
• Define conversion factor.
• Convert from one unit to
another using conversion
factors and dimensional
analysis.

•To change between units of the same
measurement scientists use conversion
factors.

•Conversion Factor – a ratio of the equality
of two different units of the same
measurement.
• Can be used to convert from one unit to
another.

1 hr = 60 min 1 min = 60 sec 1 km = 1000 m 7 days = 1 week
24 hrs = 1 day 1 kg = 2.2 lbs 1 gal = 3.79 L 264.2 gal = 1 m3
1 mi = 5,280 ft 1 kg = 1000 g 1 lb = 16 oz 20 drops = 1 mL
365 days = 1 yr 52 weeks = 1 yr 2.54 cm = 1 in 1 L = 1000 mL
0.621 mi = 1.00 km 1 yd = 36 inches 1 cc is 1 cm3 1 mL = 1 cm3

EXAMPLE
• A ruler is 12 inches long. How many
centimeters long is the ruler?

EXAMPLE
• A meter stick is 100 cm long. How
many inches is the meter stick?

EXAMPLE
• A high school cross country race is 5
kilometers. How many miles is a cross
country race?

EXAMPLE
country race? How many feet?

EXAMPLE
country race? How many feet? How
many inches?

•Temperature Conversions
• T°C = Temperature in Degrees Celsius
• T°F = Temperature in Degrees Fahrenheit
• TK = Temperature in Degrees Kelvin

EXAMPLES
•Convert the following temperatures from
Kelvin to Celsius.
𝑻 𝑪 = 𝑻 𝑲 − 𝟐𝟕𝟑
•34 K
•300 K
•214.6 K

EXAMPLES
Celsius to Kelvin.
𝑻 𝑲 = 𝑻 𝑪 + 𝟐𝟕𝟑
•49 °C
•24.3 °C
•-36 °C

EXAMPLES
Celsius to Fahrenheit.
𝑻 𝑭 = 𝟏. 𝟖𝟎 𝑻 𝑪 + 𝟑𝟐
•123 °C
•-12 °C
•47.3 °C

EXAMPLES
Fahrenheit to Celsius.
𝑻 𝑪 =
(𝑻 𝑭−𝟑𝟐)
𝟏. 𝟖𝟎
•101 °F
•36 °F
•-45 °F

1.3 Density
• Define and provide
appropriate units for mass,
volume, and density.
• Solve density problems.

1.3 Density
•Volume – the space an object occupies.
• Base Unit = Liter (L)
• Volume of Rectangular Prism = l * w * h
• Volume of a Cylinder = π * r2 * h
• Volume of a Sphere =
4
3
* π * r3
Rectangular Prism Cylinder
Sphere

1.3 Density
•Mass – a measure of the amount of
matter in an object.
• Base Unit = Gram (g)
• Mass ≠ Weight

1.3 Density
•Density - the amount of
matter present in a given
volume of substance.
• The density of a substance
always remains constant.

1.3 Density
EXAMPLE
•The five liquids in the
table were added to a
graduated cylinder.
Identify each liquid
based on the
densities provided in
the table.

1.3 Density
EXAMPLE
•A mason is trying to determine the density
of bricks to determine their quality. Each
brick has a mass of 3.00 x 103 g. Each brick
measures 15 cm x 8 cm x 45 cm. What is
the density (g/cm3) of each brick?

1.3 Density
EXAMPLE
•A shot put has a density of 7.86
grams/cm3. A shot put has a mass of
7.260 kg. What is the volume (cm3) of the
shot put? What metal is the shot put
made of?

1.3 Density
EXAMPLE
•A sample of metal has
a density of 2.699
grams/cm3. The
sample also has a
volume 18.20 cm3.
What is the mass (g)
of the metal sample?
What metal is the
sample made of?

1.4 Significant Figures
• Define uncertainty.
• Identify the number of significant
figures in a measurement.
• Round numbers to the correct
numbers of significant figures or
decimals.
• Calculate answers and determine
the proper number of significant
figures or decimals.

•Uncertainty – the possibility of error in
a measurement.
• When measurements are taken most tools
are not precise and accurate enough to
get exact measurements. To compensate
for this scientists, use significant figures.

• Significant Figure – digits that
carry meaning in a
measurement.
• Significant Figures = Sig Figs
• Sig figs are certain (known)
numbers.
• Sig figs determine how answers
are rounded during calculations.
• Sig figs are necessary in science
because they represent
measurements as accurately as
possible.

•When measurements are taken
• All certain digits are recorded.
• The last digit is uncertain and you must
estimate the digit.

•Rounding Review

EXAMPLES
•Round the following number to the
nearest thousands place.
• 8,832
• 45,832
• 625.36

EXAMPLES
nearest hundreds place.
• 11,694
• 149.49
• 38

EXAMPLES
nearest ones place.
• 893.67
• 21,232.1
• 9.3354

EXAMPLES
nearest hundredths place.
• 0.26598
• 1,612.3658
• 10

•How do you determine sig figs?

•The Atlantic Ocean
is on our right when
we look at a map.
•The Pacific Ocean is
on our left when we
look at a map.
•You are a swimmer.

• If a decimal is ABSENT
you start swimming
on the ATLANTIC side
of the number.
• You can only “swim”
through zeros.
• Once you hit a
number between 1
and 9 you stop
“swimming”.
• All the numbers left
(including zeros) are
significant.

EXAMPLES
•Determine the number of significant
figures in each number.
• 345,000
• 43,001
• 235

• If a decimal is PRESENT you
start swimming on the
PACIFIC side of the number.
• You can only “swim”
through zeros.
• Once you hit a number
between 1 and 9 you stop
“swimming”.
• All the numbers left
(including zeros) are
significant.

EXAMPLES
•Determine the number of significant
figures in each number.
• 1,230.00
• 2.3600
• 214.0001

•Multiplying and Dividing
• The answer should have the same number
of sig figs, as the number with the fewest
sig figs in your problem.

EXAMPLES
•How many significant figures should each
answer have? Calculate the answer.
• 834 * 1.002 =
• 7.3 / 2342 =
• 43 * 3.453 =

•Adding and Subtracting
• The answer should have the same number
of decimal places, as the number with the
fewest decimal places in the problem.

EXAMPLES
•How many decimal places should each
answer have? Calculate the answer.
• 834.7 + 1.002 =
• 7.3 - 2342 =
• 43.4345 + 3.453 =

EXAMPLES
•Write the following numbers in scientific
notation, using the given number of sig figs.
• 1,000,000 with two significant figures.
• 1,000,000 with three significant figures.
• 2,232,450 with two significant figures.

1.5 Scientific
Notation
• Express numbers in both
standard notation and
scientific notation.
• Solve addition, subtraction,
multiplication, and division
problems involving numbers
written in scientific notation.

1.5 Scientific Notation
•Very large and very small number are
often written in scientific notation.

•Coefficient = a number greater than or
equal to 1 and less than 10.
•Base = must be 10
•Exponent = shows the number of decimal
places that the decimal needs to moved
to change the number to standard
notation.

EXAMPLE
•The Earth is
approximately
93,000,000 miles
away from the Sun.
Write 93,000,000
miles in scientific
notation.

EXAMPLE
•A human hair is 0.00001 meters wide.
Write 0.00001 meters in scientific notation.

EXAMPLES
(2.4 ∗ 104
) + (6.8 ∗ 105
) =
(5.7 ∗ 103
) − (2.4 ∗ 102
) =

EXAMPLES
(3.2 ∗ 102
) ∗ (6.8 ∗ 107
) =
(4.5 ∗ 10−6
) ∗ (4.5 ∗ 107
) =

EXAMPLES
(9.3 ∗ 108
)
(2.3 ∗ 106)
=
(1.3 ∗ 10−8
)
(7.3 ∗ 106)
=

Unit 1 Numbers

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