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1.7: Unit 1 Practice Problems

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    Question 1.

    Give the name and symbol of the prefixes used with SI units to indicate multiplication by the following exact quantities.

    (a) 103

    (b) 10-2

    (c) 0.1

    (d) 10-3

    (e) 1,000,000

    (f) 0.000001

    Answer a

    kilo- (k)

    Answer b

    centi- (c)

    Answer c 

    deci- (d)

    Answer d

    milli- (m)

    Answer e

    Mega- (M)

    Answer f

    micro- (µ)

    Question 2.

    1 m =  __________ km?



    1 dm =  __________ m?



    One 1 m =  __________ µm?


    106 µm

    One nm =  __________  m?



    Question 3.

    Indicate the SI base units or derived units that are appropriate for the following measurements.

    (a) the length of a marathon race (26.2 miles)

    (b) the mass of an automobile

    (c) the volume of a swimming pool

    (d) the density of gold

    (f) the area of a football field

    Answer a


    Answer b


    Answer c

    cubic meter

    Answer d

    kilogram per cubic meter

    Answer c

    cubic meter

    Answer b

    square meter

    Question 4.

    50.0 inches is equivalent to how many meters? (1m = 39.37in)

    \[\mathrm{50.0\: \cancel{in.} \times \dfrac{1\: m}{39.37\:\cancel{in.}}=1.27\: m}\]

    Question 5.

    1.8 yards is equivalent to how many centimeters? (1in = 2.54cm)

    \[\mathrm{1.8\: \cancel{yrd.} \times \dfrac{36\: in}{1\:\cancel{yrd.}} \times \dfrac{2.54\: cm}{1\:\cancel{in.}}=160\: cm}\]

    Question 6.

    A car gets 23.4 mi/gal.  Express this mileage in km/L.  (1 mi = 1.61km and 1 gal = 3.785L)

    \[\mathrm{\dfrac{23.4\:\cancel{mi.}}{1\:\cancel{gal.}}\times\dfrac{1.61\: km}{1\:\cancel{mi.}}\times\dfrac{1\:\cancel{gal}}{3.785\: L}=9.95\: km/L}\nonumber \]

    Question 7. 

    The area of a table is 24.0ft2.  What is this area in dm2?  (1ft = 3.048dm)

    $$24.0ft^{2}*\left ( \frac{3.048dm}{1ft} \right )^{2}=223dm^{2}$$

    Question 8.

    The dimensions of a block are 3.46cm by 4.87cm by 102mm.  What is the volume of the block in cm3 and m3?

    Volume = 3.46cm x 4.87cm x 10.2cm = 173cm3     $$173cm^{3}*\left ( \frac{1m}{100cm} \right )^{3}=0.000173m^{3}$$

    Question 9.

    What is the density of a liquid with a mass of 31.1415 g and a volume of 30.13 cm3?


    Density = 31.145g / 30.13 cm3 = 1.034 g/cm3

    Question 10.

    What is the mass of a piece of aluminum that has a volume of 12.5mL and a density of 2.7g/cc.  


     Remember that 1mL = 1cc             M = V x D = 12.5cc * 2.7g/cc = 34g 

    Question 11.

    What is the thickness of a piece of iron foil with the dimensions of 4.8cm by 5.3cm and a mass of 0.402g?  The density of iron is 7.9g/cm3.  


    T = V/A   

    V = 0.402g/7.9g/cc = 0.051cc   

    T = 0.051cc/(4.8cm * 5.3cm)  = 0.0020cm

    Question 12.

    When a serving of mango sticky rice is tested in a bomb calorimeter, the temperature of 4.20L of water rises from 21.0ºC to 73.5ºC . How many dietary calories are in the sticky rice?  The specific heat of water is 1g/calºC .


    q=m × c ×(Tfinal−Tinitial)       

    mass of water = V * D = 4200mL * 1g/mL = 4200g       

    q = 4200g * 1cal/gºC * (73.5-21.0) =  220,500cals = 221 kcals or dietary calories


    • Christy VanRooyen, Oregon Tech
    • Adelaide Clark, Oregon Institute of Technology




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