Math Unit Fill in the blanks in your notes with the words bolded in purple .

Warm-up Question The United States is one of how many countries in the world that still use the imperial system of measurement?

3 What are the other countries?

• • Liberia Myanmar (formerly Burma)

Units of Measurement   SI Units a system of units of measurements devised around seven base units and the convenience of the number ten.

Units of Measurement  Metric System

Units of Measurement

Sample problem Move the decimal to the left

K



h



da



b



d



c



m

Move the decimal to the right Convert the following 53 hg = ________dg Start with 53.

Move the decimal 3 spaces to the right Fill in the empty spaces with zeros 53 53000 dg

Sample Problem Move the decimal to the left

K



h



da



b



d



c



m

Move the decimal to the right Convert the following 300 cg = ________kg Start with 300.

Move the decimal 5 spaces to the left 300 Fill in the empty spaces with zeros 0.00300 kg

Units of Measurement  Examples…  1000 mg =  160 cm =  109 g =  1 L =  14 km =

K



h

Move the decimal to the left 

da



b



d



c



m

Move the decimal to the right

Exit Question  Now that you are a metric master, would it be easier to convert inches to miles or centimeters to kilometer? Explain.

Warm-up Question  What is the significance of this number?

602000000000000000000000

It’s a mole!!!

(the SI unit for a amount of a substance)

Scientific Notation     Scientific notation expresses numbers as a multiple of two factors: a number between 1 and 10 (coefficient); and ten raised to a power , or exponent.

The exponent tells you how many times the first factor must be multiplied by 10.

When numbers larger than 1 are expressed in scientific notation, the power of 10 is positive .

When numbers smaller than 1 are expressed in scientific notation, the power of 10 is negative .

Exponent Coefficient

6.02 𝑥 10

23

Scientific Notation  Examples…  Change the following data into scientific notation:  The diameter of the Sun is 1,392,000 km.

1.392 𝑥 10 6 km  The density of the Sun’s lower atmosphere is 0.000000028 g/cm 3 .

2.8 𝑥 10 −8 g/cm 3

Scientific Notation      Adding and Subtracting Using Scientific Notation The exponents must be the same before doing the arithmetic. Convert the smaller number to the bigger one, by moving the decimal to the right.

Add or subtract the coefficient .

Keep the exponent the same .

Make sure your answer is written in proper scientific notation .

 Example…  1.26x10

4 kg + 2.5x10

3 kg =

Scientific Notation     Multiplying and Dividing Using Scientific Notation Multiply or divide the coefficients .

Add the exponents ( for multiplication ) or subtract the exponents ( for division ).

Examples…  (2x10 3 cm) x (3x10 2 cm) = ____________________ cm 2  (9x10 8 g) ÷ (3x10 -4 mL) =

Exit Question  Scientific notation should come in handy when expressing what kinds of quantities in chemistry?

Submicroscopic things like the size of an atom or the number of atoms in a substance.

Warm-up Question  How can you simplify this problem before you calculate the answer?

2 5 × 3 4

=

Dimensional Analysis (Factor Label)    A conversion factor values used to express the same quantity in different units.

is a ratio of equivalent A conversion factor is always equal to 1 .

   Dimensional analysis solving that focuses on the units used to describe matter.

is a method of problem Dimensional analysis often uses conversion factors.

When you convert from a large unit to a small unit , the number of units must increase .

When you convert from a small unit to a large unit , the number of units must decrease .

Factor Label Method of Conversion 100 cm = 1 m 1 m = 100 cm 100

cm

 1 1

m

1

m

100

cm

 1 Use conversion factors to systematically move from one unit to the next, cancelling out units on the diagonal in each step.

Convert 18 m = _______ cm 18m 100 cm 1 m = 1800 cm

Dimensional Analysis  Examples…  How many seconds are there in 24 hours?

24 hr 60min 1 hr 60sec 1 min = 86400 sec  A car is traveling 90.0 kilometers per hour. What is its speed in miles per minute?

90 km 1 hr 0.62mi

1 km 1 hr 60 min = 0.93 mi/min 1 km = 0.62 miles 1 hr = 60 mins 1 min = 60 secs

Exit Question On the planet Rigel, Rigellians have developed a system of measurements called S.U., or Systems Universal. Here is the conversion table for the measurements of distance: 1 gleem = 27 blops 1 blop = 34 riddigs 1 riddig = 42 chirks 1 chirk = 9 fuggles 10 fuggles = 52 hippers 2.5 hippers = 1.2 zookas 1 zooka = 7 wenzels Use the Factor Label Method and the conversions above to solve the problem.

How many fuggles are there in 19 blops?