Significant Figures Conversions and Rounding Questions

CHM-101L Measurement and Significant Figures

The ability to take proper measurements and convert values from one unit to another is a vital skill for any health care professional. On any given day a nurse may: determine the body mass of an individual, take someone’s temperature, or measure the length of an infant. It is important to know both how to utilize the tools for obtaining these measurements, and how to report the obtained values to the correct level of precision.

word image 3084

This Photo by Unknown Author is licensed under CC BY-SA-NC

As you begin your look into the concept of measurement, we first want to think about how a variety of tools can be used to obtain a desired value. Measurement tools can come in all shapes and sizes. For example, the height of a horse is measured in hands, or the unit of a foot in length is based on the length of a grown man’s foot. When using an individual’s hand or foot to measure an object, this is called measuring with a nonstandard unit.

Part A:

For this activity, you will use a pen as a nonstandard measuring device. The unit of measure will be one pen length. Select a doorway in your home and measure the width of a doorframe in pen lengths. Record your measurement below.

  1. Type of pen used: Click or tap here to enter text.
  2. Width of the doorframe in pen lengths: Click or tap here to enter text.

Now obtain a second pen and measure the same doorway with the second pen.

  1. Second type of pen used: Click or tap here to enter text.
  2. Width of the doorframe in pen lengths using pen two: Click or tap here to enter text.
  3. Did you obtain the same value for width using the two different pens? Why or why not?

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Part B:

When taking measurements in a laboratory or clinical setting, it is vital that standard tools of measure are used so that measurements can be relatable and comparable. For example, if someone says the distance was five football fields, there might be some individuals that would have difficulty conceptualizing or relating to that length. However, if the same distance were said to be 0.457 km, since a standard metric unit is utilized, the measurement would be put in a quantifiable language that everyone can associate to a particular value.

Prior to completing the next section, watch the videos relating to measurements, provided in the topic materials.

Length

Estimating the Last Digit

The maximum possible precision is defined as one tenth (1/10 or 0.1 times) the smallest division on the measuring instrument. Ruler 1 has hash marks to the ones place, so you should estimate to the tenths place. On ruler 2 the hash marks go to the tenths place, which means you should estimate to the hundredths.

Object A↓

word image 989

Object B ↑

Image: ruler from Grade 7, Unit 4.13 – Open Up Resources

  1. What is the length of Object A using the top ruler using significant figures?

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  1. What is the length of Object B using the bottom ruler using significant figures?

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  1. If you were to add lengths for questions 1 and 2, what would the combined length be using the correct amount of significant figures? (Show your work)

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Calculating Area

Measure the length and width of the box below using the printable ruler, located in the topic materials, to complete this section.

width

length

  1. Length of the box = Click or tap here to enter text. cm
  2. Width of the box = Click or tap here to enter text. cm
  3. How many places after the decimal should each of these measurements have and explain why?

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  1. If area is length times width, determine the area of the box. (Show your work)

Area = Click or tap here to enter text.

  1. How many significant figures should be in the answer to question 4?

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  1. Why? Explain the rule for significant figures in this situation.

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  1. Convert the area from cm2 to m2. Record to the proper number of significant figures.

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Volume

Go to the link provided for “Reading Graduated Cylinder,” located in topic materials. You do not need to print it out. Read the volume of liquid contained in each of the 10 graduated cylinder images and record your answers in Table 1 below.

Note: water can adhere to the sides of the graduated cylinder forming a U-shape at the top of the fluid called a meniscus. Volume measurements are read at the bottom of the meniscus.

Table 1

Graduated Cylinder

Volume

Graduated Cylinder

Volume

1

 

6

 

2

 

7

 

3

 

8

 

4

 

9

 

5

 

10

 
  1. How does changing the increment size on the graduated cylinder alter the precision of your measurement? Support your answer using examples from two graduated cylinders used in the above activity.

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  1. Give one example of an instance where a nurse would need to measure volume.

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Graphical Determination of Density

A chemistry class is asked to calculate the density of lead. The following data was gathered.

Added samples (# of cubes)

Mass (g)

Volume change (cm3)

1

5.62

0.520

2

11.43

1.068

3

17.42

1.628

4

23.15

2.169

In Excel, plot the volume change on the x-axis and the mass on the y-axis. (Refer to “Creating Graphs Using Excel: Scatterplot and Line Chart” located in the Student Success Center, as needed.)

Fit the data to a linear function.

Determine the slope and intercept values. The slope of the line is equal to the experimental value of the density of lead.

Insert a copy of the graph showing the data and the fitted line in the lab report.

  1. Slope: Click or tap here to enter text.
  2. Graph: word image 990
  3. If the accepted value for the density of lead is 11.3 g/cm, are the calculated density values for the class precise? Are they accurate? Explain your answers.

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Analysis Questions:

  1. Give one example of a nonstandard measuring device that is currently used or could be implemented into the health care system. What would this item measure?

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  1. Explain the relationship between measurements and the number of significant figures that need to be included in that measurement. What does the number of places after the decimal in a measurement tell you about the precision of the instrument that recorded them?

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  1. Will the precision of a calculation (ex. volume = L x W x H) ever be more precise than the original measurements (ex. length)? Explain your answer.

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References

Image ruler from Grade 7, Unit 4.13 – Open Up Resources, license CC BY. https://access.openupresources.org/curricula/our6-8math-v1/7/students/4/13.html

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