Significant Figures & Graphing

Guidelines for Significant Figures

Accuracy

1. The accuracy of a measurement is the difference between your measurement and the accepted value.

2. The bigger the difference between your measurement & the accepted value, the less accurate your measurement.

Precision- how finely a device is marked

1. The precision of a measurement is the size of the unit you use to make a measurement.

2. The smaller the unit, the more precise the measurement.

+ 1 cm + 0.1 cm + 0.01 cm and so on.

3. Precision is based on the device you use to make your measurement

Significant figures allow scientists to know the level of precision of a tool used to make measurements.

Rules for Significant Figures

1. All nonzero numbers are significant, so $236,596 has 6 significant figures

2. Any zero located between non-zero digits is significant, so 32,007 has 5 significant figures

3. Leading zeros at beginning of number are not significant – they are placeholders.

So, 0.000457 has 3 significant figures

4. Zeros at the end of a number with a decimal count, so 0.1750 has 4 significant figures.

5. Zeros at the end of a number without a decimal do not count, so 23,000 has 2 significant figures.

Practice Significant Figures – below are given measurements – determine the number of significant figures and then check your answers.

456.2- four / 9.06- three / 0.0045- two
4,500,000- two / 6.2000- five / 0.0030050- five

Rounding

1. If digit after place is less than 5, then round down; so 42.44 to tenths  42.4

2. If digit after place greater than or equal to 5, then round up; so 42.46 to tenths  42.5

Significant Figures with Multiplying or Dividing (MAD)

-The answer must rounded off to as many significant figures as there are in the least accurate measurement.

Division example: 4.00g /3.000 mL = 1.33333 g/mL  1.33 g/mL

Multiplication example: 12.82cm x 2.13cm x 1.86cm = 50.79027 cm3 50.8 cm3

Significant Figures with Adding or Subtracting (ASP)

-The answer must rounded off to the least precise place value.

Addition Example
215
+ 1.253
------
216.253g  216g / Subtraction Example
4,500,000
- 3
------
3,499,997  3,500,000

Graphing Guidelines

1. Make a draft sketch first with a pencil and ruler. Add color (helps with the presentation) at the end

when you have finalized your graph.

2. Place the independent variable (manipulated variable) on the x-axis (horizontal). Remember IMAX.

3. The dependent variable, that changes in response to the independent variable, goes on the y-axis

(vertical). Remember ROY.

4. Label each axis with the following: what is being graphed (time) and the units being used (seconds).

5. When choosing your scale for each axis, consider the lowest and highest values before setting the

interval.

a. Scales may or may not start at zero – you will need to determine this based on the information.

b. Every grid line on the axis should have the same value. If one grid line represents 5, then the

next line would be 10, and so on. This is called the axis scale.

c. The axis scale for the x-axis does not have to be the same as the y-axis.

d. Be sure that the scale fills most of the graph but does not run off the page.

6. It is not necessary to label every grid line; this will make it hard to read. Every fifth or tenth line is

probably adequate.

7. For a linear function, your data may not fall on the line. Use a ruler and draw a best fit line. Do not

play connect the dots.

8. For a non-linear function, for the graph make sure to sketch out a smooth best fit curve.

9. Make sure the graph has and appropriate title and your name is on it as well.

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