Ms. CuervoCAHSEE Prep

UNIT CONVERSION

Opening Activity• You are planning a graduation party for a friend, and you will be

inviting a certain number of guests. Party invitations come in packs of eight and are not sold individually.

• How will you determine how many packs to buy? What information do you need, and what steps will you take?

If you are expecting 112 guests, how many packs of invitations do you need to buy?

This problem is an example of unit conversion. You know the number of individual invitations you need, and you must find the number of packs that this is equivalent to.

Unit Conversion7MG 1.1 We will convert units of weight, length, volume, time and temperature.

VOCABULARYConvert- To express a given measurement in terms of a different unit of measurement.

Ratio- A comparison of two numbers or quantities- it may be written as a fraction.

First, we need to know a few things…

Customary Measurement

12 inches (in) = I foot (ft)3 feet = 1 yard (yd)1760 yards = 1 mile (mi)

Metric Measurement

10 millimeters (10 mm) = 1 centimeter (1 cm)100 centimeters = 1 meter (m)1000 meters = 1 kilometer (km)

Time

60 seconds (sec) = 1 minute (min)60 minutes = 1 hour (hr)24 hours = 1 day7 days = 1 week

Temperature

F = 9/5C + 32

C = 5/9 (F - 32)

Converting Common Units of Measurement

To convert from a smaller unit to a larger one, divide.

E.g. Jose is 60 inches tall = Jose is 5 feet tall.

To convert from a larger unit to a smaller one, multiply.

E.g. I studied for 4 hours = I studied for 240 minutes.

inches feet yards miles

÷12 ÷3 ÷1760

x12 x3 x1760

Converting Units of Customary Measurement

mm cm m km

÷10 ÷100 ÷1000

x10 x100 x1000

Converting Units of Metric Measurement

seconds minutes hours days

÷60 ÷24÷60

x60 x60 x7

Time Unit Conversion Chart

weeks

÷7

x24

So, remember that…

To convert from a smaller unit to a larger one, divide.

E.g. Jose is 60 inches tall = Jose is 5 feet tall.

To convert from a larger unit to a smaller one, multiply.

E.g. I studied for 4 hours = I studied for 240 minutes.

To convert from a smaller unit to a larger one, divide!

To convert from a larger unit to a smaller one, multiply!

÷

×

Example

Question: We ran 66 feet. How far is that in yards?

Step One: What is asked? Underline the question. We ran 66 feet. How far is that in yards?

Step Two: What information is given? Highlight the information.We ran 66 feet. How far is that in yards?

Step Three: Is a ratio given? If so, set up the problem. 1 yard = 3 feet

Step Four: Fill in the labels. At least one label comes from the question. Put the given ratio on one side of the multiplication sign and the other piece of information on the other. Cancel out your units as needed.

66 ft . 1 yard = 66 yards = 22 yards

3 ft 3

Step Five: Ask yourself if your answer is plausible. Does your answer seem correct?

Summary of Unit Conversion Problems

• Use proportions to solve some unit conversion problems.• Figure out what information you are given and what information is

unknown.• Select the ratio that will cancel out units to leave you with the desired

unit.• Set up the problem with the two ratios.• Solve for the desired unit.• BOOM. Done.

Guided Practice – We Got This!Question:

You want to make a banner to hang at a party. You have decided that you will need 2.8 meters of banner paper. At the store, you learn that the paper is sold by the centimeter. How many centimeters of banner should you buy?

What is asked?

What information is given?

What ratio do you need?

Cancel out your units so that you’re left with the desired unit.

Multiple-Step ConversionsQuestion: The length of the table is 3000 centimeters. What is the length is in kilometers.

1. First, convert from centimeters into meters. 2. Then, convert from meters to kilometers.

ALWAYS WORK ONE STEP AT A TIME!

3000 cm . 1 meter = 30 m 100 cm

30 m . 1 kilometer = 0.03 km 1000 m

Converting Units (Ratio Provided)

Question: Dan is driving to his house, which is 60 miles away. A mile is approximately 1.6 kilometers. How far is Dan from his house, in kilometers?

Step One: What is asked? Underline the question. Dan is driving to his house, which is 60 miles away. A mile is approximately 1.6 kilometers. How far is Dan from his house, in kilometers?

Step Two: What information is given? Highlight the information.Dan is driving to his house, which is 60 miles away. A mile is approximately 1.6 kilometers. How far is Dan from his house, in kilometers?

Step Three: Is a ratio given? If so, set up the problem. A mile is approximately 1.6 kilometers (given)

Step Four: Fill in the labels. At least one label comes from the question. Put the given ratio on one side of the multiplication sign and the other piece of information on the other. Cancel out your units as needed.

60 miles . 1.6 kilometers = 96 kilometers 1 mile

Temperature ConversionsBefore going on your bike trip, you checked the weather forecast. The average daytime temperature will be 25 degrees Celsius. What temperature is this in degrees Fahrenheit?Formula:F = 9C + 32 5Substitute the given value:F = 9(25) + 32 5

Solve using the order of operations:

F = 9(25) + 32 5F= 45 + 32= 45 + 32 = 77 degrees Fahrenheit

Guided Practice – We Got This!Question: Your friend is so excited about the party that he is counting down the seconds! He informs you that at this moment, 25,200 seconds remain until the party (…nerd). How many hours is this?

What information are you given and what information is unknown?

Remember: Work one step at a time!

Time60 seconds (sec) = 1 minute (min)60 minutes = 1 hour (hr)24 hours = 1 day7 days = 1 week

Guided Practice – We Got This!

Question: Your friend Hilda is 1.2 meters tall. How tall is Hilda in inches? (1 meter ≈ 39 inches)

What information are you given and what information is unknown?

Exit Slip

1.Convert 177 inches into yards.

2.Convert 8 meters into millimeters.

3.Convert 57 weeks into hours.