Lesson 1.06

Unit Conversion

System of Measurements

English System-Volume measured in quarts, cups, gallons

-Mass measured in pounds and ounces

-Distance measured in inches, yards, feet, miles

-hard to convert form one unit to another

Metric System- Volume measured in

liters-Mass measured in grams

-Distance measured in meters

-Easy to convert

System of measures

Unit Conversions

• Dimensional Analysis:-A problem-solving method used in physics,

chemistry, engineering, and mathematics that is based on treating units in calculations as algebraic factors or fractions.

-A way to set up math problems; unit conversions.

-Sets up multiplication and division in fraction forms.

Steps in Unit conversion

Example: How many minutes are in 2 days? 1)What are you looking for? • What unit do you want to have for your

answer? This is usually given in the problem or question being asked.

- 2 days and number of minutes2) What do you already know? • What equalities or conversions do you

already know that might help you solve the

Steps

problem? Don’t forget that you know the metric prefixes and their relationship to each base unit.

• Each step in the setup is its own conversion. The numerator must be equal to the denominator.

- 1 day = 24 hours; 1hour = 60 minutes3) Where does the information go? • Start with the given amount and its unit

Steps

and use equalities until all the units cancel except the unit you need for your final answer.

• Every equivalent can be flipped(1 hr/60 mins or 60 mins/ 1 hr)—be sure to keep each number with its correct unit, but you can switch which one is in the numerator and which one is in the denominator.

- 2 days x 24 hrs/1 day x 60 mins/ 1 hr

Steps

4) Solve it!• You multiply everything that is on top

(numerators).• Then divide by everything that is on the

bottom (denominators) to get the number that goes in your answer.

- Numerator(top) = 2 x 24 x 60 = 2880 Denominator (bottom)= 1 x 1 = 1- 2880/1 = 2880 minutes

Sample Problem

A)If your dog weighs 40 kilograms, how many milligrams does it weigh?

Step 1- 40 kg and number of milligrams(mg)Step 2- 1 kg = 10^3 g ; 10^-3g = 1 mgStep 3- 40 kg x 10^3 g/1 kg x 1 mg/10^-3 gStep 4- (top)40 x 10^3 x 1 = 40000 (bottom)1 x 10^-3 = 0.001 40000/0.001 = 40,000,000 mg

Sample Problem

B)Change the measurement 150 mm to damStep 1 -150 mm and unit damStep 2 - 1 mm = 10^-3 m ; 1 dam = 10^1 mStep 3 - 150 mm x 10^-3 m/1mm x 1 dam/

10^1 mStep 4 - 150 x 10^-3 x 1 / 1 / 10^1 = 0.015 dam

Sample Problem

C) Convert 6.5 cm/s to m/hr(unit is a fraction)Step 1- 6.5 cm/s and m/hrStep 2-1 m = 100 cm ; 1 hr = 60 mins ; 1 min = 60 secsStep 3- (convert numerator first) 6.5 cm/s x 1

m/100 cm = 0.065- you can start with the numerator first. The

one sec is still in the denominator, but you can ignore it until you get cm converted to m.

Sample Problems

- now you can continue the problem by changing the denominator from s to hr.

(convert denominator) 0.065 m/s x 60 s/1 min x 60 min/1 hr

Step 4 – (top)0.065 x 60 x 60 = 234 (bottom) 1 x 1 = 1 234 / 1 = 234 m/hr

Sample Problem

D) Convert the density 6.2 g/mL to kg/LStep 1 - 6.2 g/mL and unit kg/LStep 2 – 1000 g = 1 kg ; 1 L = 1000 mLStep 3 – 6.2 g/mL x 1kg/1000 g x 1000 mL/

1 L Step 4 – 6.2 x 1 x 1000 / 1000 / 1 = 6.2 kg/L