Chapter 10 – Measurements and Units

10.1 – U.S. Customary Units

What Measurement and Units Are and Why They Are Important

When taking measurement, we express quantities in standardized units such as pounds and yards, which enable us to compare characteristics of physical objects.

U.S. Customary Units of Length, Weight, Capacity and Time

Length Weight

Capacity Time

Conversion Examples

1. 6 qt = ____ pt2. Express 45 min in hours.3. How many cups are equivalent to 4 gal?

Adding and Subtracting Mixed Units

Some measurements involve more than a single unit. When a measurement is expressed in mixed units, we write the larger unit with the largest possible whole number.

For example, 3 hr 5 min should not be written as 2 hr 65 min

Only quantities with the same units can be added or subtracted.

Conversion Examples

1. Convert 3 lb 8 oz to ounces.2. Change 328 min to hour and minutes.3. Find the sum of 8 ft 4 in and 4 ft 10 in.4. Subtract 4 yds 2 feet from 7 yds 1 foot.5. Add 3 yds 2 in to 2 feet 3 inches.6. The length of a sidewalk is 12 ft 2 inches. The

width of the sidewalk is 3 ft 4 inches. What is the difference between the length and width?

10.2 – Metric Units and Metric/U.S. Customary Unit Conversion

The Metric System

Developed about 200 years ago by a French scientist, but is now the standard in most countries for medicine, science, and many other fields.

Length/Distance: MeterWeight/Mass: GramCapacity/Volume: Liter

The Metric SystemOther units are formed by multiplying or dividing the base units by 10.

Base Units

Length/Distance: MeterWeight/Mass: GramCapacity/Volume: Liter

Length: MeterThe millimeter is about the thickness of a dime.

The centimeter is approximately the width of your little finger.

The meter is a little longer than a yard.

Weight: Gram

The milligram is the smallest unit, about the weight of a hair.

The gram is approximately the weight of a raisin.

The kilogram is a about 2 pounds or the weight of the textbook.

Capacity: Liter

The milliliter is the smallest unit, about as much as an eyedropper contains.

The liter is slightly more than a quart.

Conversions

You can use the same process we used for converting U.S. units or use the following conversions.

Examples

1. 2.4 g = ____ mg2. 700 m = ____ km3. 7 L = ____ ml4. Express 5 km in millimeters.5. Which is the most appropriate for the length

of a pencil? (a) 20 mm, (b) 20 cm, (c) 20 m.6. Vitamin C commonly comes in pills with a

strength of 500 mg. How many of the pills will an adult need to take if she wants a dosage of half a gram?

Metric/U.S. Customary Unit Conversions

Examples

1. Express 4 oz in grams.2. Express 12 cm in inches3. 6 qt = ____ L4. A prehistoric bird had a wingspan of 8 m.

Express this wingspan in feet.

10.2b – Basic Geometry Conversions

- Length is an expression of a distance along a line, such as the perimeter around your house.

- What is the perimeter of these figures?

3 ft

2 ft3 ft 3 ft

1 ft

10.2b – Basic Geometry Conversions

- Area is the number of square units a two-dimensional figure contains, such as the floor of your house.

- Determine the area of the figures below and then convert them to in2. One ft2 = 144 in2. Why is this?

3 ft

2 ftA lw1

2A bh

5 ft

4 ft

10.2b – Basic Geometry Conversions

- Volume is the number of cubic units required to fill a three-dimensional figure, such as the amount of space inside your refrigerator.

- Determine the volume of the figure below and convert it to in3. One ft3 = 1728 in3. Why is this?

2 ft3 ft

5 ft

V lwh

r = 2 ft

h = 4 ft2V r h

r is the radius of the circular top.