Measurement

Way of expressing a value as the product of a number between 1 and 10 and a power of 10

Ex. 602,000,000,000,000 can be written 6.02x1014

Scientific Notation

Include digits that are known, plus a last digit that is estimated

Rules:◦ Every nonzero digit in a reported measurement is

significant. Ex 24.7m, 0.743m, 714m◦ Zeros appearing inbetween of nonzero digits are

significant. Ex. 7003m, 40.79m, 1.503m◦ Leftmost zeros appearing in front of nonzero digits

are not significant. They are placeholders. Ex. 0.0071m, 0.42m, 0.000099m You can eliminate placeholders by writing in scientific

notation

Significant Figures

Rules◦ Zeros at the end of a number and to the right of a

decimal point are always significant. Ex. 43.00m, 1.010m, 9.000m

◦ Zeros at the rightmost of a measurement that lie to the left of an understood decimal point are not significant if they serve as a placeholder. Ex. 300m, 7000 m, 27,210m Use Scientific notation to show zeros are significant,

Ex. 3.00x102

Significant Figures (cont)

Rounding◦ Decide on the amount of sig figs the answer

should have◦ Round to that number counting to the left◦ If the number to the right of the last sig fig is less

than 5 the number is dropped◦ If the digit is more than 5 then the last sig fig is

rounded up by 1

Using Significant Figures in Calculations

Addition and Subtraction◦ Should be rounded to the same number of

decimal places as the measurement with the least number of decimal places

Multiplication and Division◦ Round the answer to the same number of sig figs

as the measurement with the least number of sig figs

Sig Fig Calculations (cont)

Precision- gauge of how exact a measurement is.◦ The more sig figs a measurement has the more

precise it is Accuracy- closeness of a measurement to

the actual value of what is being measured

Precision and Accuracy

Precision Accuracy

The metric system is a measurement system based on our decimal (base 10) number system.

Other countries and all scientists and engineers use the metric system for measurement.

The Metric System

Metric Prefixes Metric Units The metric system has prefix modifiers that are

multiples of 10.

Prefix Symbol Factor Number Factor Word

Kilo- k 1000 Thousand

Hecto- h 100 Hundred

Deca- da or dk 10 Ten

Unit m, l, or g 1 One

Deci- d .1 Tenth

Centi- c .01 Hundredth

Milli- m .001 thousandth

Place Values of Metric Prefixes

Thousand

Hundred Ten One Tenth

Hundredth

Thousandth

kmkgkL

hmhghL

dkmdkgdkL

mgL

dmdgdL

cmcgcL

mmmgmL

Meters

Meters measure length or distance

One millimeter is about the thickness of a dime.

Meters One centimeter is

about the width of a large paper clip

•or your fingernail.

A meter is about the width of a doorway

Meters

A kilometer is about six city blocks or 10 football fields.

1.6 kilometers is about 1 mile

Meters

Gram

Grams are used to measure mass or the weight of an object.

Grams

A milligram weighs about as much as a grain of salt.

Grams

1 gram weighs about as much as a small paper clip.

1 kilogram weighs about as much as 6 apples or 2 pounds.

Liters

Liters measure liquids or capacity.

Liter

1 milliliter is about the amount of one drop

Liter

1 liter is half of a 2 liter bottle of Coke or other soda

A kiloliter would be about 500 2-liter bottles of pop

Liter

To change from one unit to another in the metric system you simply multiply or divide by a power of 10.

Changing Metric Units

To change from a larger unit to a smaller unit, you

need to multiply.1 km x 1000 = 1000 m

1 m x 100 = 100 cm1 cm x 10 = 10mm

Place Values of Metric Prefixes

Thousand

Hundred Ten One Tenth

Hundredth

Thousandth

kmkLkg

hmhLhg

dkmdkLdkg

mLg

dmdLdg

cmcLcg

mmmLmg

Move the decimal point to the right to multiply.

To change from smaller units to larger units you

divide by a power of ten.

1000mm ÷ 10 = 100cm100cm ÷ 10 = 10dm

10dm ÷ 10 = 1m

Place Values of Metric Prefixes

Thousand

Hundred Ten One Tenth

Hundredth

Thousandth

kmkLkg

hmhLhg

dkmdkLdkg

mLg

dmdLdg

cmcLcg

mmmLmg

Move the decimal point to the left to divide.

Measure of how hot or cold an object is When 2 objects are close heat will transfer

from the hotter object to the cooler object When temperature increases substances

will expand. When temperature decreases substances

will contract

Temperature Properties

Symbol for Fahrenheit is °F Freezing point of water is 32°F Boiling point of water is 212°F

Measuring Temperature in Fahrenheit

Symbol for Celsius is °C Freezing point of water is 0 °C Boiling point of water is 100 °C

Measuring Temperature in Celsius

Symbol for Kelvin is K Freezing point of water is 273 K Boiling point of water is 373 K

Measuring Temperature in Kelvin

°C = 5/9 (°F-32.0°) °F = 9/5 (°C) + 32.0°

Converting Fahrenheit and Celsius

K= °C +273 °C = K – 273

Converting Celsius and Kelvin

Conversions

Conversion factors are a way to express the one quantity in different ways

◦ Ex. 1 dollar = 4 quarters= 10 dimes= 20 nickels=100 pennies

◦ Ex. 1 meter= 10 decimeters= 100 centimeters= 1000 millimeters

Conversion

Ratio of equivalent measurements

◦ 2 dollars = 20 dimes = 1 2 dollars 2 dollars

◦ 1 meter = 100 centimeters = 1 1 meter 1 meter

Conversion Factors

How many seconds are in a workday that lasts exactly eight hours?

Example

What is 0.073cm in micrometers?

Example

The mass per unit volume of a substance in a property called density. The density of manganese, a metallic element, is 7.21 g/cm3. What is the density of manganese expressed in units kg/m3?

Example

Density

Ratio of the mass of an object to is volume Density = mass/volume Density depends on what the substance is

made of not how much of the substance you have

Ex 10.0 cm3 piece of lead has a mass of 114 g. What is the density?

Determining Density

As temperature increases, the volume of a substance increases

Since volume increases, then the density will decrease as the temperature increases

Density and Temperature

Volume = mass/density

Mass = density X volume

Calculating volume and mass from density