do now: calculate the following. a)(1.3 x 10 3 ) + (8.1 x 10 3 ) b)(9.4 x 10 6 ) – (5.3 x 10 6 )...

Do Now: Calculate the following.

a)(1.3 x 103) + (8.1 x 103)

b)(9.4 x 106) – (5.3 x 106)

c)(5.0 x 104) x (3.1 x 102)

d)(6.3 x 109) (2.1 x 106)

Do Now: Calculate the following.

a)(1.3 x 103) + (8.1 x 103) = 9.4 x 103

b)(9.4 x 106) – (5.3 x 106) = 4.1 x 106

c)(2.0 x 104) x (3.1 x 102) = 6.2 x 106

d)(6.3 x 109) = 3.0 x 103

(2.1 x 106)

YWBAT

• Explain what happens when a measurement is multiplied by a conversion factor

• Describe the kinds of problems that can be easily solved using dimensional analysis.

Quantities can usually be expressed in several different ways.

Quantities can usually be expressed in several different ways.

1 dollar = 4 quarters = 10 dimes

1 dollar= 20 nickels = 100 pennies

The same thing is true for scientific quantities.

1 meter = 10 decimeters = 100 centimeters

1 meter = 1000 millimeters

These are all different ways to express the same length.

Conversion Factors

A conversion factor is a ratio of equivalent measurements (aka – Funny Form of 1)

Conversion Factors

When a measurement is multiplied by a conversion factor, the numerical value is usually changed but the actual size of the quantity measured remains the same.

Unit Prefixes

Conversion Factors

What conversion factor would you use if you wanted to convert 9 teaspoons to tablespoons?

Conversion FactorsWhat conversion factor would you use if you wanted to convert 9 teaspoons to tablespoons?

1 tablespoon = 3 teaspoons

Conversion factor = 1 tablespoon 3 teaspoons

9 teaspoons x 1 tablespoon = 3 tablespoons 3 teaspoons

Conversion Factors

What about significant figures?

•Remember – Conversion factors are defined or exact quantities.•They have an unlimited number of significant figures and do not affect the rounding of a calculated answer.

Dimensional Analysis

Dimensional Analysis is a way to analyze and solve problems using the units, or dimensions, of the measurements.

Dimensional Analysis

If the exchange rate between U.S. dollars and euros is 0.890379 euro to every dollar, what is the conversion factor that allows you to convert from U.S. dollars to euros?

Dimensional Analysis

If the exchange rate between U.S. dollars and euros is 0.890379 euro to every dollar, what is the conversion factor that allows you to convert from U.S. dollars to euros?

The conversion factor to convert from U.S. dollars to euros would be

0.890379 Euro1 US Dollar

Dimensional Analysis

A complex problem may need more than one step.

When converting between units, it is often necessary to use more than one converison factor.

Dimensional Analysis

The diameter of a sewing needle is 0.073 cm. What is the diameter in micrometers?

Dimensional Analysis

The diameter of a sewing needle is 0.073 cm. What is the diameter in micrometers?

Dimensional Analysis

The diameter of a sewing needle is 0.073 cm. What is the diameter in micrometers?

Dimensional Analysis

The directions for an experiment ask each student to measure 1.84 g of copper (Cu) wire. The only copper wire available is a spool with a mass of 50.0 g. How many students can do the experiment before the copper runs out?

Dimensional Analysis

The directions for an experiment ask each student to measure 1.84 g of copper (Cu) wire. The only copper wire available is a spool with a mass of 50.0 g. How many students can do the experiment before the copper runs out?