Measurements, Unit Conversion, and Scientific Notation

Vocabulary and key conversion facts from the lecture on measurements and scientific notation.

Measurements

The quantification of physical quantities using standard units to enable communication, comparison, and calculation.

Common Measurable Quantities

Length, Mass, Time, Temperature, and Volume.

Length Conversion (Kilometer to Meter)

$$1\,km = 1000\,m$$

Length Conversion (Meter to Centimeter)

$$1\,m = 100\,cm$$

Length Conversion (Centimeter to Millimeter)

$$1\,cm = 10\,mm$$

Mass Conversion Fact

$$1\,kg = 1000\,g$$

Time Conversion (Hour to Minutes)

$$1\,hour = 60\,minutes$$

Time Conversion (Minute to Seconds)

$$1\,minute = 60\,seconds$$

Time Conversion (Hour to Seconds)

$$1\,hour = 3600\,seconds$$

Method of Unit Conversion Steps

Identify Factor, Multiply by 1, and Cancel Units.

Scientific Notation

A way to express numbers as $a \times 10^n$, where $1 \le a < 10$ and $n$ is an integer.

Speed of Light (Scientific Notation)

$3 \times 10^8\,m/s$ (representing $300,000,000\,m/s$)

Earth to Sun Distance (Scientific Notation)

$9.3 \times 10^7\,miles$ (representing $93,000,000\,miles$)

Nanometer (Scientific Notation)

$1 \times 10^{-9}\,m$ (representing $0.000000001\,m$)

Scientific Notation for 0.00045

$$4.5 \times 10^{-4}$$

Conversion Result: 72 km/h to m/s

$$20\,m/s$$

Conversion Result: 5000 mg to Scientific Notation

$$5 \times 10^0\,g$$

Conversion Result: 0.003 hr to Scientific Notation

$1.08 \times 10^1\,s$ (calculated from $10.8\,s$)