V. Units of Measurement

VI. Metric System

Quantity - number + unit

UNITS MATTER!!UNITS MATTER!!

Quantity Base Unit Abbrev.

Length

Mass

Time

Temp

meter

kilogram

second

kelvin

m

kg

s

K

Amount mole mol

Symbol

l

m

t

T

n

mega- M 1x106

deci- d 1x10-1

centi- c 1x10-2

milli- m 1x10-3

Prefix Symbol Factor

micro- 1x10-6

nano- n 1x10-9

kilo- k 1x103

BASE UNIT ---

457 dm = km

457 dm = mm

1) 20 cm = ______________ m

2) 0.032 L = ______________ mL

3) 45 km = ______________ dm

4) 805 cm = ______________ km

0.2

0.00805

450,000

32

VII. Dimensional Analysis

You will be using these converstions throughout the year, so its best to take the time to memorize them now.

1.00 in = 2.54 cm2.2 lbs = 1.00 kg1.1 qts = 1.00 L

metric from earlier table

Steps:

1. Identify starting & ending units.

2. Line up conversion factors so units cancel.

3. Multiply all top numbers & divide by each bottom number hit enter.

4. Check units & answer.

3

3

cm

g

1

cm

In algebra In algebra abab What do we do?What do we do? b b

In scienceIn science called factor-label methodcalled factor-label method◦ Units, or “labels” are canceled, or “factored” out

g

Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off?

Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off?

8.0 cm 1 in

2.54 cm= 3.2 in

How many milliliters are in 1.00 quart of milk?

How many milliliters are in 1.00 quart of milk?

1.00 qt 1 L

1.057 qt= 946 mL

qt mL

1000 mL

1 L

Eastview football needs 550 cm for a 1st down. How many yards is this?

Eastview football needs 550 cm for a 1st down. How many yards is this?

550 cm 1 in

2.54 cm= 6.0 yd

cm yd

1 ft

12 in

1 yd

3 ft

A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?

A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?

1.3 m 100 cm

1 m= 86 pieces

m pieces

1 piece

1.5 cm

You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3.

You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3.

lb cm3

1.5 lb 1 kg

2.2 lb= 35 cm3

1000 g

1 kg

1 cm3

19.3 g

A favorite item at the fair is bacon on a stick. If each stick holds approximately 0.15kg of bacon and the booth serves an average of 45 people an hour, how many pounds of bacon are consumed in the 12 days of the fair? (The gates open at 6:00am and close at midnight.)

Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also!

Best way: Square or cube the ENITRE conversion factor

Example: Convert 4.3 cm3 to mm3

4.3 cm4.3 cm33 (10 mm) (10 mm) 33

(1 cm)(1 cm) 3 3 = 4.3 cm4.3 cm33 10 1033 mm mm33

1 133 cm cm33

= 4300 mm3

1000 cm3 (1 dm)3

(10 cm)3 = 1 dm3

So, a dmSo, a dm33 is the same as a Liter ! is the same as a Liter !

A cmA cm33 is the same as a milliliter. is the same as a milliliter.

How many liters of water would fill a container that measures 75.0 in3?

How many liters of water would fill a container that measures 75.0 in3?

75.0 in3 (2.54 cm)3

(1 in)3= 1.23 L

in3 L

1 L

1000 cm3