Chapter 2, Part 1 Notes

Chapter 2: Unit Conversions and Manipulations

• Answers in chemistry consist of three parts: a number, an indication of accuracy, and units.

Exact Numbers

• Exact numbers include:

  • Things you count (e.g., ears, chins, eyes, eggs, fingers, thumbs, pieces of paper).

  • Things converted from one metric set of units to another metric set of units (e.g., $1.234 \text{ km} = 1234 \text{ meters} = 123400 \text{ millimeters}$).

  • Exact conversions within the imperial system (e.g., $3 \text{ feet} = 1 \text{ yard}$).

  • Kelvin conversion number: $273.15$ is an exact number.

  • $0$ °C conversion: $32$ is an exact number.

  • $2.54 \text{ cm}$ exactly equals $1 \text{ inch}$. This is the only exact metric to imperial conversion.

Inexact Numbers

Addition and Subtraction

• The sum or difference has the same indication of accuracy as the least accurate of the figures added or subtracted.

  • Example:

    • $12.34 \text{ cm}$ (Accurate to the hundredths place)

    • $5.6 \text{ cm}$ (Accurate to the tenths place)

    • $12.9 \text{ cm}$ (Answer is only accurate to the tenths place)

Multiplication and Division

• The product or dividend has the same number of significant digits as the least of the multiplicands or divisors.

Significant Digit Rules

• If a number has all non-zero digits, all digits are significant (e.g., $1.234$ has $4$ SF).

• If a number has leading zero(s), they do not count (e.g., $0.0123$ has $3$ SF).

• If a number has zeros between two non-zero numbers, they count (e.g., $1.02345$ has $6$ SF).

• If a number has trailing zeros, they count (e.g., $1.000$ has $4$ SF).

• Exception: Zeros to the right of non-zero digits in numbers without decimals are ambiguous (e.g., $330$ has $2$ SF, but $330.$ has $3$ SF).

Rounding Rules

• Round up if the last significant figure digit is five or greater.

• Do not round up if the last significant figure is $0$, $1$, $2$, $3$, or $4$.

• A bar over the last significant figure is a simple way of indicating the last significant figure (i.e., no need to round).

  • Example: $5.3935 \text{ cm}$

Conversions

• Examples:

  • Convert $1.234 \text{ inches}$ to $\text{mm}$.

  • How many grams does a $0.25 \text{ pounder}$ hamburger weigh in grams?

  • How many miles is $4.345 \text{ mm}$?

• Conversions are performed using a specific "method"