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Significant Figures and Conversions

INTRODUCTION

Units are essential in all industrial and career settings.  Once a measurement is taken or made, the corresponding correct units must be applied so that the reader and user of the data are aware of the number and associated quantities.  Remember the Mars Climate Orbiter (R.I.P. brave orbiter).

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Significant figures arise from the fact that all numbers inherently have only a finite amount of accuracy and precision when a measurement or calculation is made.  There are very specific rules on how many significant figures (or significant digits) may be kept during a measurement or calculation.

The purpose of this lab is to gain a greater comprehension of how to convert data between metric and English measurements, as well as learning the process of identifying and recording significant figures. Complete each task and record your findings in each data section below.

Upon completion, save this document as a PDF with your name in the filename in the form “Yournamehere-Conversions.pdf” and upload to the assignment box on online campus.

 

Unit Conversions

Length
1 in = 2.54 cm
1 ft = 30.5 cm
1 m = 39.37 in = 3.28 ft
1 mi = 1.609 km = 1609 m
1 fermi = 1 femtometer (fm) = 10-15 m
1 angstrom (Ǻ) = 10-10 m
Volume
1 liter (L) = 1000 mL = 1000 cm3 = 1 x 10-3 m3
Mass
1 kg = 2.20 lb
1 atomic mass unit (u) = 1.6605 x 10-27 kg

 

 

Force
1 lb = 4.45 N
1 N = 105 dyne
Energy and Work
1 cal = 4.184 J
1 eV = 1.6 x 10-19 J
Power
1 hp = 550 ft·lb/s = 746 W
Pressure
1 atm = 760 mm Hg
1 atm = 101.3 kPa
1 atm = 14.7 psi

 

PROCEDURE

A reminder of rules regarding Significant Figures (s.f.):

  1. All non-zero numbers are significant
  2. Captive zeroes are significant.
  3. Leading zeroes are never significant.
  4. Trailing zeroes are significant if a decimal point is shown, and not significant if there is not one
  5. When adding/subtracting, leave the same number of decimal places in the answer as there are in the number with the least s.f.
  6. When multiplying/dividing, your answer should have the same number of s.f. in the quantity with the least number of s.f. In essence, you don’t want your answer to be more significant than any value that went into it.

 

Setting Up a Problem for a Units Conversion:

Given Number with Units Conversion Factor = Target Number with Target units

 

  1. Identify the given units and the target units
  2. Select a conversion factor that contains the given units and the target units
  3. At the conversion factor term, arrange a ratio of the two equivalent numbers such that the units can mathematically cancel the given units and replace the given units with the target units.
  4. Perform the mathematical operation

 

Practice Examples

  1. Determine the number of significant figures in each of the following values. (Example: a) 0.00021 has 2 significant figures, therefore the answer is: 2.) (1 pt each for 6 pts total)

 

  1. a) 0.00021 2 significant figures
  2. b) 0.23500 Click here to enter text. significant figures
  3. c) 2.8970 x 103 Click here to enter text. significant figures
  4. d) 1.289003 x 10-4 Click here to enter text. significant figures
  5. e) 0.02900450 Click here to enter text. significant figures
  6. f) 1.000234 Click here to enter text. significant figures
  7. g) 0.04890 x 104 Click here to enter text. significant figures
  8. Perform the indicated operations and round your answers with the proper number of significant figures according to rules in Chapter 1. (1 pt each for 3 pts total)

 

112.98566

323.2367

23.239

+21.2567

Click here to enter text.

(112.98566)(4.674)(2.209) = Click here to enter text.

(9.21)(5.348)(5.235)2 = Click here to enter text.

 

  1. Perform the following conversions by multiplying the given term by the appropriate conversion factor. (1 pt each for 4 pts total)
  2. a) 345 km = Click here to enter text. meters

 

  1. b) 34.22 mm = Click here to enter text. cm

 

  1. c) 0.65 g = Click here to enter text. mg

 

  1. d) 124.8 mL = Click here to enter text. liters

 

  1. Convert the following using the conversion factors provided, don’t forget the units as part of your answer. (1 pt each for 4 pts total)
    1. 23 m/min to ft/sec Click here to enter text. ft/sec

 

  1. 98 N/m² to lb/ft² Click here to enter text. lb/ft²

 

  1. 3 km/hr to miles/hr Click here to enter text.. miles/hr

 

  1. 57 psi to mm Hg Click here to enter text. mm Hg

 

  1. Convert the following using the conversion factors provided, don’t forget the units as part of your answer. (1 pt each for 3 pts total)
  2. Convert 250 mm2 to m2 Click here to enter text. m2

 

  1. Convert 1 km3 to m3 Click here to enter text. m3

 

  1. Convert 9.8 m/s2 to km/hr2 Click here to enter text. km/hr2

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