Units and Significant Figures

Measure in appropriate units, convert between units, and report justified precision.

Lesson 2 of 33 parts Practice Flashcards

1/3

Units and Dimensional Analysis

Objective: Select SI units and convert quantities by canceling units.

The SI base unit for length is the meter, for mass the kilogram, and for time the second; laboratory work often uses grams, milliliters, and degrees Celsius. A derived unit combines base units. A conversion factor is a ratio equal to one, such as 100 cm/1 m. Dimensional analysis places the unwanted unit in the denominator so it cancels; the remaining unit checks the setup. Conversion does not change the measured quantity.

Formulas

$1 m = 100 cm$
$1 L = 1000 mL$

Worked examples

Try itConvert 2.5 m to centimeters.Show answer

1. Write the conversion: 1 m = 100 cm. 2. Set up 2.5 m × (100 cm / 1 m). 3. Cancel m and multiply: 250 cm.

Swipe sideways to move between sections

Units and Dimensional Analysis

Objective: Select SI units and convert quantities by canceling units.

Formulas

$1 m = 100 cm$
$1 L = 1000 mL$

Worked examples

Try itConvert 2.5 m to centimeters.Show answer

1. Write the conversion: 1 m = 100 cm. 2. Set up 2.5 m × (100 cm / 1 m). 3. Cancel m and multiply: 250 cm.

Significant Figures

Objective: Count significant figures and round reported measurements appropriately.

Significant figures represent measured digits justified by an instrument plus one estimated digit. Nonzero digits are significant; zeros between nonzero digits are significant; leading zeros are not; trailing zeros after a decimal point are significant. In multiplication and division, report as many significant figures as the least precise factor; in addition and subtraction, round to the least precise decimal place. Exact counted values and defined conversions do not limit precision.

Worked examples

Try itCompute 2.4 cm × 3.15 cm with proper precision.Show answer

1. Multiply: 2.4 × 3.15 = 7.56. 2. The first factor has two significant figures. 3. Round 7.56 to two significant figures: 7.6 cm².

Precision, Uncertainty, and Units

Objective: Report calculations with units and justified precision.

Resolution is the smallest interval an instrument displays or distinguishes; uncertainty describes plausible variation around a measured value. Accuracy concerns closeness to a reference value; precision concerns repeatability. For measured products or quotients, retain guard digits during calculation and round at the end. Units must be carried through each step, and a result without compatible units is not a valid physical answer.

Formulas

$density = mass / volume$

Worked examples

Try itA sample has mass 24.0 g and volume 8.0 mL. Find density.Show answer

1. Write density = mass / volume. 2. Substitute: 24.0 g / 8.0 mL = 3.0 g/mL. 3. Report two significant figures because 8.0 has two.

You finished the reading!

Lock it in with a few practice questions, then move on to the next lesson.

Practice Next lesson

Previous lessonProperties and Changes of Matter Next lessonLaboratory Measurements and Safety