The color was brownish

The volume was 6 mL

The weight was 11.5 g

What’s the difference between these three pieces of data?

Quantitative – a piece of data that reports a number measured.

Quantitative = Quantity.

Mass, volume, temperature, speed, area, etc.

Qualitative – a piece of data describing something without measuring a value.

Qualitative = Quality.

Color, texture, odor, taste, sound, etc.

Qualitative or Quantitative?

The pavement is rough

The reaction turned red

It’s 93 °C outside

Qualitative

Qualitative

Quantitative

Freezing point of water is 0 °C.

If you measured it and got 0.3°C, your measurement would be accurate.

If you measured it and got 17 °C, it would not be accurate.

Precision vs. Accuracy

Accuracy is a measure of how close a measurement is to the actual/true value.

If you are comparing 2 or more numbers and trying to determine if they are accurate or not, you take the average and compare it to the accepted number.

Three measurements are made to determine the freezing point of water: 0.3 °C, 0.2 °C, 0.1 °C.

Average = 0.2 °C, which is very close to 0 °C, so it’s accurate data.

Three measurements are made to determine the freezing point of water: -30 °C, 13 °C, 14 °C.

Average = -1 °C, which is very close to 0 °C, so it’s accurate data.

What’s different about the two sets of data?

For example if you measured the temperature of boiling water 3 times and got: 120 °C, 120 °C, 119 °C, 121 °C, what would you guess the 5th measurement would be approximately?

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

Precision is a measurement of reproducibility.

However, if you measured:80 °C, 120°C, 140 °C, 60 °C, would you be able to guess what the 5th measurement would be?

In the examples, which set of data is precise?

Practice Problems

A scientist measures the density of water four times and gets:1.0 g/mL, 2.5 g/mL, 2.6 g/mL, 0.1 g/mL, and 5.2 g/mL.

Is the data accurate? Is the data precise?

Another group of scientists measures the density of water four times and gets:3.3 g/mL, 3.4 g/mL, 3.0 g/mL, 3.5 g/mL.

Is the data accurate? Is the data precise?

Error is the difference between the value obtained from an experiment and the accepted value.

Think of it as “how far off” you are.

Error

If you measure the temperature outside and get 77 °C, but then look online and the national weather service says it’s 79 °C, how far off are you?

In equation form:

Error = (experimental value) – (accepted value)

A lot of the time it’s more important to look at the error in relationship to the accepted value more closely.

If you took a test and were 5 points from a perfect score, is that good or bad? What more do you need to know?

You need to know how many points were possible. Getting only 1/6 is not a good score. However, 195/200 is a very good score.

In science how we make this comparison generally is with % error.

For % error, we take the error calculated above (taking the absolute value) and divide it by the accepted value. This gives us a ratio of error-to-accepted. We then multiply by 100 to make it a percent.

In equation form, % error is:

% Error = ____|error|_____ x 100 accepted value

Step 1: Calculate Error = 229 g – 250 g = -21 g

What’s the percent error a measurement of 229g when the accepted value is 250 g?

Step 2: Take absolute value = |-21 g| = 21 g

Step 3: Make a Ratio = 21 g/250 g = 0.084

Step 4: Turn into a percent by multiplying by 100: 0.084 x 100 = 8.4 % error

The last reported number in measurements is a best guess, or in other words is uncertain.

When making measurements you always make a “best guess” one digit beyond what an analog instrument shows.

Which of the 2 drawings has more liquid?

How would you report these 2 measurements?

Which numbers do you know for certain and which ones are a “best guess”?

Significant Figures – a measurement including all of the digits that are known plus one last digit that’s estimated.

Measurements must always be reported with the correct number of “sig figs” because you often have to do calculations, like density, and the answers of those calculations depend on the number of sig figs in the measurements.

Significant Figures

1) Every non-zero digit reported is assumed to be significant. Volume of 1446 mL, 0.8717 mL and 243.9 mL all have 4 sig figs.

Sig Fig Rules

There are 3 types of zeros: Leading, Embedded, and Trailing

2) Leading Zero’s are never significant, they are only placeholders.

0.000278 g, 0.0986 g and 0.952 g all have only 3 significant figures

Sig Fig Rules

3) Embedded zeros are always significant

101 mL has 3 significant figures, 0.009002 L has 4 significant figures

4) Trailing zeros are only significant if they are after a decimal point, otherwise they are just placeholders

100 g had only 1 significant figure

1010 g has 3 significant figures

0.009050 g has 4 significant figures

How many sig figs in the following measurements?

1) 10.909 mL

2) 0.909 mL

3) 1.909 mL

4) 21.210 mL

5) 0.00100 g

6) 3030 m

Practice Problems

Sig Fig Rules

5) Finally, there are 2 cases where there are unlimited sig figs.

Counting. If I could the students in class, I know that number exactly, and because of that there are unlimited sig figs: 16.00000000000….

Exactly defined quantities. For example, 60 min in 1 hour, 100 cm in 1 m, etc. This is important for calculations, which we will work on tomorrow.

Scientific notation is a way of writing any number as the product of two numbers: “a coefficient and 10 raised to a power”.

b) The power of 10 is the direction and number of places to move the decimal point.

a) The coefficient is always a number equal to or greater than 1 and less than 10:

• 1 ≤ coefficient < 10

• One and only one digit to the left of the decimal point (can’t be zero)

Scientific Notation

For Example:

• 101 in scientific notation would be 1.01 x 102

• 0.0074 would be 7.4 x 10-3

Two benefits of scientific notation:

1) Easier way to write very big or very small numbers: 557,000,000,000 = 5.57 x1011 and 0.0000000022 = 2.2 x 10-9

2) Easy way to determine sig figs. Every number in the coefficient is a sig fig.

If you aren’t sure on a sig fig problem, ask yourself “how would this be written in scientific notation? 3000 = 3 x103 so only 1 sig fig, 0.0000000022 = 2.2 x 10-9, so only 2 sig figs, 30100 = 3.01 x 104 so only 3 sig figs.