Unit Tracks

1Set up the conversion

2Calculate

…

Multiply everything on top, multiply everything on the bottom, then divide. Enter what your calculator shows, or type the calculation itself as an expression.

Unlocks once the setup is marked correct.

3Round to the correct significant figures

Unlocks once step 2 is marked correct.

Reference

Everything needed for these questions. Units are case-sensitive: Mg is a megagram, mg is a milligram.

Metric prefixes

Prefix	Symbol	Meaning
giga	G	10⁹ = 1 000 000 000
mega	M	10⁶ = 1 000 000
kilo	k	10³ = 1000
deci	d	10⁻¹ = 0.1
centi	c	10⁻² = 0.01
milli	m	10⁻³ = 0.001
micro	µ	10⁻⁶ = 0.000 001
nano	n	10⁻⁹

A prefix multiplies the base unit: 1 Mg = 10⁶ g, 1 km = 1000 m, 1 cm = 0.01 m (so 100 cm = 1 m). Written as a factor, the 1 goes with the prefixed unit: 1000 m over 1 km, or 1 km over 1000 m.

What the units mean

m	meter, the base unit of length
g	gram, the base unit of mass
s	second, the base unit of time
L	liter, volume (1 L = 1000 mL = 1000 cm³)
Mg, kg, mg	megagram (10⁶ g), kilogram (10³ g), milligram (10⁻³ g)
km, cm, mm	kilometer (10³ m), centimeter (10⁻² m), millimeter (10⁻³ m)
in, ft, yd, mi	inch, foot, yard, mile
min, hr, day	minute, hour, day
grain	an old mass unit; 15.432 grains = 1 g
furlong	an old length unit; 8 furlongs = 1 mi
fortnight	two weeks; 1 fortnight = 14 days
cm/s	centimeters per second: cm on top, s on the bottom
km³	cubic kilometers: km × km × km, three factors of km

Conversion factors

Length

1 in = 2.54 cm	exact
1 ft = 12 in	exact
1 yd = 3 ft	exact
1 mi = 5280 ft	exact
1 mi = 1.6093 km	5 sig figs
8 furlongs = 1 mi	exact

Mass

1 lb = 453.6 g	4 sig figs
1 kg = 2.205 lb	4 sig figs
1 lb = 16 oz	exact
1 g = 15.432 grains	5 sig figs

Volume

1 L = 1000 mL	exact
1 mL = 1 cm³	exact
1 qt = 0.9464 L	4 sig figs
1 gal = 4 qt	exact

Time

1 min = 60 s	exact
1 hr = 60 min	exact
1 day = 24 hr	exact
1 week = 7 days	exact
1 fortnight = 14 days	exact

Significant figures

Nonzero digits always count. Zeros between nonzero digits count (1.005 has 4).
Leading zeros never count (0.0025 has 2).
Trailing zeros count only when there is a decimal point (1.20 has 3, 120 has 2, 120. has 3).
When multiplying or dividing, round the answer to the fewest sig figs of any measured value.
When adding or subtracting, round to the decimal place of the least precise value: 12.52 g + 3.1 g = 15.6 g.
Exact conversions (1 km = 1000 m, 1 in = 2.54 cm, 60 s = 1 min) never limit sig figs.
Use scientific notation for very large or small answers: 1.80e12 means 1.80 × 10¹² and has 3 sig figs.

Typing tips

One unit per box. Put the unit you are dividing by in the bottom box.
Squares and cubes: type m3, m^3 or m³.
Powers of ten: type 3.00e8 or 3.00x10^8.
Press Enter to jump to the next box.
Calculator: the round button in the corner opens it. Type or tap keys, press Enter for the result, and use Insert to drop it into the answer box you were working in.
Calculator, Cylinder tab: find the volume, diameter or length of a cylinder from the other two, with every step shown, including the algebra.
Free mode: the end unit and sig figs are worked out from your chain. Type in either box to pin your own; clear it to go back to auto.
Free mode: hover or tap the Sig figs box to count the sig figs value by value, mark exact conversions, and check your conclusion.
Free mode: + given adds a second line for problems like 3.68 min + 8.00 s → hr. Convert every line to the same unit; the lines are then added. Tap the + between lines to make it a −.
Free mode: once all three steps are correct, Save as a question keeps the conversion, finished work included, as a numbered question you can look over or clear and redo.
Add a question with the + button: give a value, its unit, and the unit to convert to. Units can be compound, like cm/s or km^3. For a sum or difference, add another given to the question.

Unit Tracks

New question

1Set up the conversion

2Calculate

3Round to the correct significant figures

Save this conversion as a question