# 1.7: Unit 1 Practice Problems

### 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

kilo- (k)

centi- (c)

deci- (d)

milli- (m)

Mega- (M)

micro- (µ)

### Question 2.

1 m =  __________ km?

0.001km

1 dm =  __________ m?

0.1m

One 1 m =  __________ µm?

106 µm

One nm =  __________  m?

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

(c) the volume of a swimming pool

(d) the density of gold

(f) the area of a football field

meter

kilogram

cubic meter

kilogram per cubic meter

cubic meter

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

## Contributors

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