Measurement & Problem Solving - Chapter 2 (Global Temperature)

Vocabulary flashcards covering key concepts from measurement, uncertainty, units, sig figs, density, volume, and unit analysis.

Measured numbers

Inexact or approximate numbers that include uncertainty (e.g., 5.25 m, 500 L, 75 g).

Exact numbers

Counts that have no uncertainty; infinite sig figs (e.g., 75 m&m’s in a bowl, 24 students in a class).

Measurement

Comparison of a physical quantity to be evaluated with a unit; always include units when available.

Unit

A standard quantity used to express measurements (e.g., m, cm, s, g).

Uncertainty

Inherent doubt in any measurement due to instrument limits; not all digits are certain.

Accuracy

Closeness of a single measurement to its true value.

Precision

Closeness of a set of measurements to each other.

Ruler

A length-measuring instrument; degree of uncertainty depends on the ruler’s hash marks (more marks = less uncertainty).

Graduated cylinder

A laboratory instrument used to measure volumes of liquids; read at the bottom of the meniscus.

Pipet (pipette)

A device used to deliver a fixed volume of liquid; read from calibration marks.

Buret

A long calibrated glass tube with a stopcock used for precise delivery of liquids during titrations.

Meniscus

The curved surface of a liquid in a graduate instrument; read at the bottom of the curve.

Uncertainty range (volumetric instruments)

Typical uncertainty ranges: graduated cylinder +0.1 to +0.5 mL; pipet +0.1 to +0.01 mL; buret +0.1 to +0.01 mL.

Exponential numbers

A notation for very large or very small numbers using powers of ten (10^n).

Scientific notation

Expression of a number as a × 10^n, where 1 ≤ a < 10.

Exponent

The power of ten in scientific notation; indicates scale of the number.

Significant figures (sig figs)

Digits that carry meaning about precision; the last digit is uncertain.

Leading zeros

Zeros to the left of the first nonzero digit; not significant.

Zeros between nonzero digits

Zeros between nonzero digits are significant.

Trailing zeros after a decimal

Zeros to the right of a decimal point after a nonzero digit are significant.

Trailing zeros before a decimal (ambiguous)

Zeros at the end of a number before the decimal point are ambiguous; use scientific notation to clarify.

Scientific notation and sig figs

The number of sig figs equals the number of digits in the coefficient; the exponent does not affect sig figs.

Rounding (sig figs)

Adjusting the last significant figure based on the next digit (≥5 round up; ≤4 round down).

Decimal places rule (addition/subtraction)

Result should have the same number of decimal places as the measurement with the least decimals.

Significant figures rule (multiplication/division)

Result should have as many sig figs as the measurement with the least number of sig figs.

Unit analysis

Method of carrying units through calculations to ensure correct final units and cancel unwanted units.

Unit factor

A ratio of two equivalent quantities used to convert units (e.g., 1 dollar/10 dimes).

Unit equation

Statement of equivalence that provides two unit factors (e.g., 1 dollar = 10 dimes).

Exactly equivalent relationships

Two units that are exactly equal to one another; have infinite sig figs (e.g., 1 L = 1000 mL, 1 ft = 12 in).

Exact equivalents

Conversions that are defined exactly (infinite sig figs); English and metric units are not all exact equivalents.

Conversion factor

A ratio that relates two different units and contains exact equivalences used to convert measurements.

Mass

The amount of matter in a substance; measured in grams with a balance.

Weight

The force of gravity acting on an object; on a balance, gravity acts equally on both sides.

Volume

Amount of space occupied by a solid, liquid, or gas; units include L, mL, cm^3.

1 mL = 1 cm^3

Common equivalence used interchangeably for volume.

Volume by displacement

Method to measure volume of an irregular solid by the difference in liquid volume before and after immersion.

Density

Mass per unit volume (d = mass/volume); typical units are g/mL, g/cm^3 for liquids and solids, g/L for gases.

Density of water

A reference density of 1.00 g/mL at 25°C; objects denser than water sink, less dense float.

Percent

Percent = part/whole × 100; expresses a ratio as a fraction of 100.

Percent concept example

Used to describe composition, e.g., silver vs copper in sterling silver by mass.

Metric prefixes (large)

Prefixes indicating powers of ten: tera (10^12), giga (10^9), mega (10^6), kilo (10^3), hecto (10^2), deka (10).

Metric prefixes (small)

Prefixes indicating powers of ten: deci (10^-1), centi (10^-2), milli (10^-3), micro (10^-6), nano (10^-9), pico (10^-12).

Basic units and symbols (metric/English)

Common base units and symbols: meter (m), liter (L), gram (g), second (s) and their English counterparts.

Volume formula for a rectangular solid

Volume = length × width × height (V = l × w × h); ensure consistent units.

1 cm^3

Equal to 1 mL in volume.

Volume in different units (conversion practice)

Convert between volume units (e.g., L, mL, cm^3) using exact conversion factors.

Mass vs. volume consistency

When calculating volume or density, ensure units are compatible and cancel appropriately.

Density as a unit factor

Using density to relate mass and volume; rearrange equations to solve for desired quantity.