Chapter 3Scientific Measurement

Using & Expressing Measurements

A measurement is a quantity that has both a number and a unit. Ex. 25 mg, 4 L

Scientific Notation- when a given number is written as the product of two numbers: a coefficient and 10 raised to a power

Example 0.000038742

Answer: 3.8742 x 10-5

Example 6872355482.3Answer: 6.87 x 109

Accuracy, Precision, and Error

Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured.

Ex. the boiling point of water is 1000C In an experiment you measured it at 99.80C

Would this be considered accurate?

Precision is a measure of how close a series of measurements are to one another

Ex. Three groups measured the mass of the same substance.Group 1 - 89.4 g Group 2 – 89.3 g Group 3 – 89.5 g

These measurements are considered precise

Accuracy, Precision, and Error

Some measurements can be accurate, precise, both or neither.

For the previous example, if the mass of the substance was actually 80.1 g. the measurements would be precise but not accurate.

If the mass was 89.45 g, then the measurements would be both precise and accurate

Determining Error

Error = experimental value - accepted value

Experimental value: value measured in a lab

Accepted value: correct value given by reliable sources

% Error = error

accepted valueX 100

Significant Figures in Measurements

The significant figures in a measurement include all the digits that are known, plus a last digit that is estimated.

Measurements must always be in significant figures.

6 rules for determining significant figures

P. 66-67

Significant Figures in Calculations

In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated.

Addition & Subtraction:

The answer for an addition and subtraction calculation should be rounded to the same number of decimal places as the measurement with the least number of decimal places

Sample Problem 3.2

Significant Figures in Calculations

Multiplication and Division:You need to round the answer to the

same number of significant figures as the measurement with the least number of significant figures.

Sample problem 3.3

Section 2The International System of Units

Measuring with SI Units

The metric system was developed in

1795.

Revised in 1960 & called The

International System of Units (SI)

Consists of seven base units.

Table 3.1

Measuring with SI Units

Length - SI unit is the meter (m)

When appropriate, you may use km, cm, or um.

Mass - SI unit is the kilogram (kg)

Weight is a force that measures the pull of gravity on a given mass

Objects can become weightless but never massless

Measuring with SI Units

Volume - The SI unit is the amount of space occupied by a cube that is 1 meter on each side. (1 m3)

The metric unit is the liter (L).

1 mL is equal to 1 cm3.

Therefore, you can use these

measurements interchangeably.

Measuring with SI Units

Temperature – measure of how much heat an object has

Heat will always move from a object of higher temp to an object with lower temp.

Most substances expand with an increase in temp and contract with a decrease in temp.

Exception is Water

Measured by Celsius or Kelvin

Celsius - Water freezes at 0oC and boils at 100oC

Kelvin - Water freezes at 273.15 K and boils at 373.15 K

Measuring with SI Units

Energy – SI unit is the Joule (J)

The capacity to do work

One calorie is the quantity of heat

that raises the temperature of 1 g water by 1oC.

The food you eat is measured in

Kilocalories

1 J = 0.2390 cal 1 cal = 4.184 J

Section 3Conversion Problems

Conversion Factors

A conversion factor is a ratio of equivalent measurements

Ex. 4 quarters = 1 dollar

When a measurement is multiplied by a conversion factor, the numerical value is generally changed, but the actual size of the quantity measured remains the same.

Use a process of dimensional analysis to set up the problem and solve it.

Dimensional Analysis

Dimensional Analysis is a way to

analyze and solve problems using

the units, or dimensions, of the measurements.

Sample problem 3.5

Dimensional analysis provides you

with an alternative approach to

problem solving

Sample problem 3.6

Multistep Problems

Some problems require more then one step in order to solve.

Example

A man ran across the country for three years straight.

How many hours of running did he do?

Step 1 – convert years into days

Step 2 – covert days into hours.

Sample problem 3.8

Converting Complex Units

Many measurements are expressed as a ratio of two units such as m/s

Using dimensional analysis you can convert these measurements just as easily as it is to convert 1 unit measurements

Example:

Convert 45 km/h into m/s

Answer = 12.5 m/s

Sample problem 3.9

Section 4Density

Determining Density

Density is the ratio of the mass of an object to its volume

When calculating density the mass must always be in gram and the volume in cm3

Density is an intensive property that depends only on the composition of a substance, not on the size of the sample

Determining Density

Density determines what will float

and what will sink.

Example:

A helium filled balloon will float because helium is less dense then the air.

A balloon blown up by you will sink,

because carbon dioxide is more dense then air.

Density and Temperature

As you know from section 2, volume usually increases as temperature increases

Therefore, density usually decreases as its temperature increases

The exception is water.

As the temperature of water increases density also increases.

This is why ice floats on water.

Sample problem 3.10