Chapter 1: Calculations, Formulas & Measurement

When adding or subtracting measurements, how do I round my final answer?

Round to the same number of decimal places as the measurement with the fewest decimal places.

-

Shortcut: + / − → decimal places

When multiplying or dividing measurements, how do I round my final answer?

Round to the same number of significant figures as the measurement with the fewest significant figures.

-

× / ÷ → sig figs

Do leading zeros count as significant figures?

No. Leading zeros are zeros before the first nonzero digit.

-

Example: 0.0032 = 2 SF

Do zeros between nonzero digits count as significant figures (Interior) ?

Yes.

-

Example: 309 = 3 SF

When do trailing zeros count as significant figures?

Trailing zeros after a decimal point are significant.

-

Example: 49.000 = 5 SF

Trailing zeros with an implied decimal can be ambiguous.

Example: 2700 = ambiguous

What are the rounding rules for this chemistry course?

• Next digit 4 or less → leave it

• Next digit 5 or greater → round up

• Exactly 5 → round up

• Don't round until the end of a multi-step calculation

What does the ³ in cm³ mean, and what does cm³ measure?

³ means “cubed.”
cm³ = cubic centimeters, a unit used to measure volume.

• cm → length

• cm² → area

• cm³ → volume

• 1 cm³ = 1 mL

Memory trick: ³ = 3 dimensions (length × width × height) = volume

How is a number written in scientific notation?

Write it as:

coefficient × 10ⁿ

The coefficient must be between 1 and 10.

Examples:

• 2400 = 2.4 × 10³

• 0.00086 = 8.6 × 10⁻⁴

What is the SI unit for length?

meter (m)

What is the SI unit for mass?

kilogram (kg)

What is the SI unit for temperature?

Kelvin (K)

How are milliliters (mL) and cubic centimeters (cm³) related?

1 mL = 1 cm³

How many mL and cm³ are in 1 L?

L = 1000 mL = 1000 cm³

If I'm given mass and volume, how do I calculate density?

Divide mass by volume.

d= m/v

d = density, m = mass, V = volume

If I'm given density and volume, how do I calculate mass?

Multiply density × volume.

m=dV​

Mass = Density × Volume

f I'm given mass and density, how do I calculate volume?

Divide mass by density.

V= m/d

Volume = Mass ÷ Density

What density units should I know?

• Solids → g/cm³

• Liquids → g/mL

• Gases → g/L

• SI unit → kg/m³

How do I set up a unit conversion using dimensional analysis?

Multiply by a conversion factor arranged so the unit you DON'T want cancels, leaving the unit you DO want.

Example:

1.07 kg× 1000g/1kg

The kg cancels, leaving grams.

What SI prefixes and powers of 10 should I know?

• tera (T) = 10¹²

• giga (G) = 10⁹

• mega (M) = 10⁶

• kilo (k) = 10³

• centi (c) = 10⁻²

• milli (m) = 10⁻³

• micro (µ) = 10⁻⁶

• nano (n) = 10⁻⁹

• pico (p) = 10⁻¹²