MEASUREMENT IN THE SCIENTIFIC METHOD

Good experiments have good measurements with properly recorded data.

Bad measurements create incorrect data. Incorrect data = bad results = wrong conclusions.

HIT THE TARGET

WHAT MAKES A GOOD MEASUREMENT?

Accuracy – how close your measurement is to the

correct value

Precision – how close one measurement is to all other

measurements in the experiment

ERROR

ALL MEASUREMENTS HAVE ERROR-Error is a measure of how far off you are

from correct Error mainly comes from measuring

tools. Accuracy depends on the tools used.

ERROR

A guess must be made when recording error…

How long is the box?

0 1 2 3 4 5 6 7 8

I know the measurement is at least 5 cm…

cm But since there are not marks between the

centimeters, that is all we know for sure…

So we guess…5.8cm, the last digit shows our guessSince each person guesses different, the last digit

shows our error

ERROR

When reading measurement data you can tell where the guess was made by how many decimal places the measurement has…more decimal places = more accurate

The guess is ALWAYS the last digit

ERROR

To Get less error, we use a tool with smaller guesses…

0 1 2 3 4 5 6 7 8

What is the measurement with a more accurate tool?5.91 cm…the 1 is a guess

MINIMIZING ERROR

Use precise and accurate tools – your measurement can only be as precise & accurate as your tool.

Using proper measuring technique

USING MEASUREMENTS

Since our measurements all have error, when we use them in calculations, we have to carry the error through…

How do we do this you ask?

Significant Figures…

SIGNIFICANT FIGURES

Significant figures - show accuracy in measurements & calculations

JUST BECAUSE IT IS ON YOUR CALCULATOR SCREEN DOES NOT MAKE IT SIGNIFICANT!

RULES FOR IDENTIFYING SIG. FIGS. IN A MEASUREMENT

All non-zero digits are significant1, 2, 3, 4, 5, 6, 7, 8, 9

Leading zeros are place holders and not significant

0.0000000000000000002

Trailing zeros are only significant if they are to the right of the decimal

1000000 zeros are not significant1.00000 zeros are significant

Zeros between two significant figures, or between a significant digit and the decimal are significant

101 zero is signigicant10.0 all zeros are significant

10000. all zeros are significant

SIGNIFICANT FIGURES

So, is there an easy way to figure this out without memorizing the rules…

SIG FIG TOOL

AP

We will use our great nation to identify the sig figs in a number…

On the left of the US is the Pacific and on the right is the Atlantic

SIG FIG TOOL

AP

If we write our number in the middle of the country we can find the number of sig figs by starting on the correct side of the country…

If the decimal is Present, we start on the Pacific sideIf the decimal is Absent, we start on the Atlantic sideWe then count from the first NON zero till we run out of digits…

0.05600

SIG FIG TOOL EXAMPLES

AP 105200

This number has _____ sig figs

4

SIG FIG TOOL EXAMPLES

AP 105200.

This number has _____ sig figs

6

CALCULATIONS WITH SIGNIFICANT FIGURES

Since our measurements have error, when we use them in calculations, they will cause our answers to have error.

Our answer cannot be more accurate than our least accurate measurement.

This means that we have to round our answers to the proper accuracy…

CALCULATIONS WITH SIGNIFICANT FIGURES

When we add or subtract, our error only makes a small difference. So, when adding or subtracting we base our rounding on the number of decimal places.

Rule for Adding and Subtracting – the answer must have the same number of

decimal places as the measurement used in the calculation that has the fewest decimal places

CALCULATIONS WITH SIGNIFICANT FIGURES

When we multiply or divide, our error makes a large difference. So, when multiplying or dividing numbers, we round based on significant figures.

Rule for Multiplying and Dividing – the answer must have the same number of

significant figures as the measurement used in the calculation that has the fewest significant figures

EXAMPLE 1

35.0 cm + 2.98 cm – 7 cm = ?30.98 cm

This is what your calculator gives you…However, as we just discussed, the answer cannot be

more accurate than your least accurate measurement…

The least accurate measurement is 7 cm…So by the adding rule, our answer must be rounded

to zero decimal places, or the ones placeWhich gives us the answer of

31 cm

EXAMPLE 2

3.0 x 89.54 ÷ 0.000000001 = ?268620000000

We have to round to proper sig figs…So we get

300000000000Or in scientific notation

3 x 1011

EXAMPLE 3

What if we have both add/sub and mult/div in the same problem?

(2.4 m + 5 m) ÷ (1.889ss – 3.9 s) = ?Order of opperations means we do the addition

and subtraction first…(7.4 m) ÷ (-2.011s)

We have to round these before we go on to the division…

7 m ÷ -2.0 sNow divide

-3.5 m/sNow Round

-4 m/s

THE ENDPresentation created by:

Mr. Kern

Information gathered from years of scientific research and data collection

Assignment provided by :Glencoe Publishing Company