1.3 PRESENTING SCIENTIFIC DATA
Key Terms – scientific notation, precision, accuracy, significant figures
Line graphs are best for displaying continuous changes of two data
One set of data is the independent variable because the scientist controls it. It goes on the xaxis.
The other set of data is the dependent variable because it changes as the independent variable
changes. The dependent variable depends on the independent variable. It goes on the y-axis.
A bar graph compares data for several individual items or events.
Pie charts show the parts of a whole
WRITING NUMBERS IN SCIENTIFIC NOTATION
Scientific notation is a method of expressing a quantity as a number multiplied by 10 to the
appropriate power.
To convert a number with many digits into scientific notation, move the decimal point until you
reach a number between and including one and smaller than ten. Write this number down, and
then write an “x 10?.” Replace question mark with the number of spots you moved the decimal
point. If you moved to the left, the number will be positive; right, negative.
Example: 18 000 L = 1.8 x 104
0.0000056 m = 5.6 x 10-6
To convert from scientific notation to long form, do the reverse:
If the superscript is positive, move the decimal that number of places to the right; negative, to the
left. To check, turn the long form back into scientific notation.
Example: 5.4 x 10-5 = 0.000054
9.8 x 103 = 9 800
Using scientific notation
When you multiply two values in scientific notation, you multiply the bases and add the powers
of 10. Examples: 5.3 x 102 x 1.7 x 108 = 9 x 1010
When you divide, you divide the bases and subtract the powers of 10. Example below
USING SIGNIFICANT FIGURES
When you use measurements in calculations, the answer is only as precise as the least precise
measurement used in the calculation - the measurement with the fewest significant figures.
Significant figures are all the digits of a measurement known with certainty plus one final digit,
which is somewhat uncertain or is estimated.
Rules for Determining Significant Zeros
When you look at the number in question, you must determine if it has a decimal point or not. If
it has a decimal, you should think of "P" for "Present". If the number does not have a decimal
place, you should think of "A" for "Absent".
Example, for the number 35.700, think "P", because the decimal is present.
For the number 6500, you would think "A", because the decimal is absent.
Now, the letters "A" and "P" also correspond to the "Atlantic" and "Pacific" Oceans,
respectively. Now, assume the top of the page is North, and imagine an arrow being drawn
toward the number from the appropriate coast. Once the arrow hits a nonzero digit, it and all of
the digits after it are significant.
Example 1. How many significant digits are shown in the number 20 400 ? (remember that we
use spaces, rather than commas, when writing numbers in Science.
Well, there is no decimal, so we think of "A" for "Absent". This means that we imagine an
arrow coming in from the Atlantic ocean, as shown below;
20 400 ←
The first nonzero digit that the arrow hits would be the 4, making it, and all digits to the left of it
significant.
Answer - There are three significant digits in the number 20 400
Here are the significant digits, shown in boldface. 20 400
Example 2. How many significant digits are shown in the number 0.090 ?
Well, there is a decimal, so we think of "P" for "Present". This means that we imagine an arrow
coming in from the Pacific ocean, as shown below;
 0.090
The first nonzero digit that the arrow will pass in the 9, making it, and any digit to the right of it
significant.
Answer - There are 2 significant digits in the number 0.090
Here are the significant digits, shown in boldface. 0.090
When performing calculations, the answer should have the same number of significant figures
that the value with the fewest number of significant figures has.
Accuracy and Precision
Accuracy is the closeness of measurements to the correct or accepted value of the quantity
measured.
Precision is the closeness of a set of measurements of the same quantity made in the same
way.
The figure shows graphs of four measurements of water masses. Part (a) has high accuracy and
precision. Part (b) is precise, but not very accurate. Part (c) is accurate, but not very precise. Part
(d) shows both poor accuracy and precision.