1.3metric System

SCIENTIFIC MEASUREMENT

The Metric System

Measuring • The numbers are only half of a measurement. • It is 10 long. • 10 what? • Numbers without units are meaningless. • How many feet in a yard? • A mile? • A rod?

The Metric System • Easier to use because it is a decimal system. • Every conversion is by some power of 10. • A metric unit has two parts. • A prefix and a base unit. • prefix tells you how many times to divide or multiply by 10.

Base Units • • • • • • •

Length - meter - more than a yard - m Mass - grams - about a raisin - g Time - second - s Temperature - Kelvin or ºCelsius K or ºC Energy - Joules- J Volume - Liter - half of a two liter bottle- L Amount of substance - mole - mol

• • • • • • • • •

Prefixes

kilo k 1000 times deci d 1/10 centi c 1/100 milli m 1/1000 micro μ 1/1000000 nano n 1/1000000000 kilometer - about 0.6 miles centimeter - less than half an inch millimeter - the width of a paper clip wire

Volume • calculated by multiplying L x W x H • Liter the volume of a cube 1 dm (10 cm) on a side • 1L = 1 dm3 • so 1 L = 10 cm x 10 cm x 10 cm • 1 L = 1000 cm3 • 1/1000 L = 1 cm3 • 1 mL = 1 cm3

Volume • 1 L about 1/4 of a gallon - a quart • 1 mL is about 20 drops of water or 1 sugar cube

Mass • Weight is a force. Mass is the amount of matter. • 1 gram is defined as the mass of 1 cm3 of water at 4 ºC. • 1000 g = 1000 cm3 of water • 1 kg = 1 L of water

Mass • 1 kg = 2.5 lbs • 1 g = 1 paper clip • 1 mg = 10 grains of salt

Converting

k h D

d c m

• how far you have to move on this chart, tells you how far, and which direction to move the decimal place. • The box is the base unit, meters, Liters, grams, etc.

Conversions

k h D

d c m

• Change 5.6 m to millimeters ●starts at the base unit and move three to the right. ●move the decimal point three to the right

56 00

Conversions

k h D • • • •

d c m

convert 25 mg to grams convert 0.45 km to mm convert 35 mL to liters It works because the math works, we are dividing or multiplying by 10 the correct number of times.

Conversion factors • “A ratio of equivalent measurements.” • Start with two things that are the same. One meter is one hundred centimeters • Write it as an equation. 1 m = 100 cm • Can divide by each side to come up with two ways of writing the number 1.

Conversion factors 1m 100 cm

=

100 cm 100 cm

Conversion factors 1m 100 cm

=

1

Conversion factors 1m 100 cm 1m 1m

=

=

1 100 cm 1m

Conversion factors 1m 100 cm

1

= =

1 100 cm 1m

Conversion factors • A unique way of writing the number 1. • In the same system they are defined quantities so they have unlimited significant figures. • Equivalence statements always have this relationship. • big # small unit = small # big unit • 1000 mm = 1 m

Write the conversion factors for the following • kilograms to grams • feet to inches • 1.096 qt. = 1.00 L

What are they good for? • We can multiply by one creatively to change the units . • 13 inches is how many yards? • 36 inches = 1 yard. • 1 yard = 36 inches • 13 inches x

1 yard 36 inches

=

What are they good for? We can multiply by one creatively to change the units . ■ 13 inches is how many yards? ■ 36 inches = 1 yard. ■ 1 yard =1 36 inches ■ 13 inches x 1 yard = 36 inches ■

Conversion factors • Called conversion factors because they allow us to convert units. • Really just multiplying by one, in a creative way. • Choose the conversion factor that gets rid of the unit you don’t want.

Sample Problems • Perform the following unit conversions: • 12 in. to centimeters • 3.76 hr to minutes • 137 J to calories • 0.085490 atm to pascals

Sample Problems • Perform the following unit conversions: • 0.001348 g to milligrams • 3560 N to kilonewtons • 5.29 cs to seconds