Metric Prefixes

PrefixSymbolValue
gigaG10⁹
megaM10⁶
kilok10³
hectoh10²
decada10¹
(unit)1
decid10⁻¹
centic10⁻²
millim10⁻³
microμ10⁻⁶
nanon10⁻⁹
picop10⁻¹²

Essential Unit Equalities

Volume
1 kL = 1 m³1 L = 1 dm³
1 mL = 1 cm³

Volume Formulas for Geometric Objects

ObjectFormulaVariables
Cube$V = a^3$$a$ = side length
Rectangular Prism$V = l \times w \times h$$l$ = length, $w$ = width, $h$ = height
Sphere$V = \frac{4}{3}\pi r^3$$r$ = radius
Cylinder$V = \pi r^2 h$$r$ = radius, $h$ = height
Cone$V = \frac{1}{3}\pi r^2 h$$r$ = radius, $h$ = height
Triangular Prism$V = \frac{1}{2} \times b \times h \times l$$b$ = base, $h$ = height of triangle, $l$ = length
Pyramid$V = \frac{1}{3} \times A \times h$$A$ = base area, $h$ = height

Material Densities

MaterialDensity (kg/m³)
Gold19 300
Silver10 490
Lead11 340
Copper8 960
Brass8 600
Aluminum2 700
Polyethylene900
Oak (wood)700
Cork250

1. Convert 62,5 mL to the SI and give the results in scientific notation as a·10<sup>b:</sup> (1 point)

a ) Value of a

b ) Value of b

2. Convert 4200000 kA to the SI and give the results in scientific notation as a·10<sup>b:</sup> (1 point)

a ) Value of a

b ) Value of b

3. Convert 4.23·10⁷ g/m to the SI and give the results in scientific notation as a·10<sup>b:</sup> (1 point)

a ) Value of a

b ) Value of b

4. Convert 180 km/h to the SI and give the results in scientific notation as a·10<sup>b:</sup> (2 points)

a ) Value of a

b ) Value of b

5. Convert 20 kg/L to the SI and give the results in scientific notation as a·10<sup>b:</sup> (3 points)

a ) Value of a

b ) Value of b

6. Convert 11.1 g/m² to the SI and give the results in scientific notation as a·10<sup>b:</sup> (2 points)

a ) Value of a

b ) Value of b

7. Convert these temperatures between K and °C: (4 points)

a ) 20 ºC = ? K

b ) -10 ºC = ? K

c ) 200 K = ? °C

d ) 400 K = ? K

8. Calculate the density of each object in SI units (kg/m³) and determine what material it most likely is using the table in the theory section. (4 points)

a ) Earring: mass = 125 g; volume from immersion = 62 mL → 73 mL. Give density in kg/m³ (rounded to nearest integer).

b ) Earring: Using the density you calculated, what is the most likely material?

c ) Ball: mass = 240 g; diameter = 8 cm. Give density in kg/m³ (rounded to nearest integer).

d ) Ball: Using the density you calculated, what is the most likely material?