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

(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?

Answer: 0.001km

1 dm = __________ m?

Answer: 0.1m

One 1 m = __________ µm?

Answer: 10⁶ µm

One nm = __________ m?

Answer: 10^-9nm

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

(d) the density of gold

(f) the area of a football field

Answer a: meter
Answer b: kilogram
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)

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

Question 5.

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

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

Question 6.

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

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

Question 7.

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

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

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?

Answer: 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?

Answer: 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.

Answer: 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.

Answer

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 .

Answer

q=m × c ×(T_final−T_initial)

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

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

Contributors

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