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?

What are the other countries?

3

• 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

Convert the following 53 hg = ________dg

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

mcdbdahK Move the decimal to the right

Move the decimal to the left

Sample Problem

Convert the following 300 cg = ________kg

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

mcdbdahK Move the decimal to the right

Move the decimal to the left

Units of Measurement Examples…

1000 mg = __________ g

160 cm = __________ mm

109 g = __________ kg

1 L = __________ mL

14 km = __________ m

1

1600

0.109

1000

14000

mcdbdahK Move the decimal to the right

Move the decimal to the left

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.

6.02 𝑥1023Coefficient

Exponent

Scientific Notation Examples…

Change the following data into scientific notation: The diameter of the Sun is 1,392,000 km.

The density of the Sun’s lower atmosphere is 0.000000028 g/cm3.

km

g/cm3

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… 1.26x104 kg + 2.5x103 kg = ____________________ kg1.51x 104

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…

(2x103 cm) x (3x102 cm) = ____________________ cm2

(9x108 g) ÷ (3x10-4 mL) = ____________________ g/mL

6 x 105

3 x 1012

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?

=

Dimensional Analysis (Factor Label) A conversion factor is a ratio of equivalent

values used to express the same quantity in different units. A conversion factor is always equal to 1.

Dimensional analysis is a method of problem-solving that focuses on the units used to describe matter. 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

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

100 cm = 1 m 1 m = 100 cm 11

100

m

cm 1100

1

cm

m

18m 100 cm

1 m

= 1800 cm

Dimensional Analysis

Examples… How many seconds are there in 24 hours?

A car is traveling 90.0 kilometers per hour. What is its speed in miles per minute?

1 km = 0.62 miles 1 hr = 60 mins 1 min = 60 secs

24 hr 60min

1 hr

60sec

1 min= 86400 sec

0.62mi

1 km

1 hr

60 min

= 0.93 mi/min90 km1 hr

Exit QuestionOn 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 blops1 blop = 34 riddigs1 riddig = 42 chirks1 chirk = 9 fuggles10 fuggles = 52 hippers2.5 hippers = 1.2 zookas1 zooka = 7 wenzels Use the Factor Label Method and the conversions above to solve the problem. 

How many fuggles are there in 19 blops?