Standards and Measurement

Standards and Measurement

Why is Measurement Important?

Measurement helps us describe sizes, weights, and temperatures in a way everyone can understand. It is used in daily life, science, trade, and industry to make accurate calculations.

Reading a Measuring Device

There are two types of measuring devices:

  1. Digital devices – Show exact values, like a digital scale displaying weight in grams.

  2. Non-digital devices – Require estimation, like a ruler where you must guess between two marks.

Rule for Recording Measurements:

  • Digital devices: Write all digits shown.

  • Non-digital devices: Write the certain digits plus one estimated digit.

Significant Figures (Sig Figs)

Sig figs show how precise a measurement is.

Rounding Rules:

  1. Round down if the digit after the last significant fig is less than 5. (e.g., 54.623 → 54.62)

  2. Round up if the digit after the last significant fig is greater than 5. (e.g., 54.528 → 54.53)

  3. If the digit is 5, round to the nearest even number. (e.g., 54.625 → 54.62)

Scientific Notation:

Used to express very large or small numbers:

  • Example: 9,200,000,000,000 → 9.2 × 10²⁴

  • Example: 0.000048 → 4.8 × 10⁻⁵

Counting Significant Figures:

  • Non-zero digits are always significant (e.g., 56.78 → 4 sig figs).

  • Zeros between numbers are significant (e.g., 402.6 → 4 sig figs).

  • Zeros before numbers are NOT significant (e.g., 0.06034 → 4 sig figs).

  • Zeros after a decimal are significant (e.g., 812.90 → 5 sig figs).

Basic and Derived Quantities

  1. Base Quantities (Cannot be simplified further):

    • Length (m), Mass (kg), Time (s), Temperature (K), etc.

  2. Derived Quantities (Combinations of base quantities):

    • Velocity (m/s), Volume (m³), Density (kg/m³).

Metric vs. English System

  • Metric System (SI): Used worldwide, based on powers of 10 (e.g., 1 meter = 100 cm).

  • English System: Used in the US (e.g., inches, pounds, miles).

Metric Prefixes

Prefix

Symbol

Value

Example

Kilo

k

1,000

1 km = 1,000 m

Centi

c

0.01

1 cm = 0.01 m

Milli

m

0.001

1 mm = 0.001 m

Micro

µ

0.000001

1 µm = 10⁻⁶ m

Nano

n

0.000000001

1 nm = 10⁻⁹ m

Conversions

  • Convert by multiplying by conversion factors:

    • Example: 1 km = 1000 m → Multiply by (1000 m / 1 km) to cancel km.

Mass vs. Weight

  • Mass: The amount of matter in an object (same everywhere).

  • Weight: The force of gravity on an object (changes with location, like on the Moon).

Density (Mass ÷ Volume)

  • Formula: Density = Mass / Volume

  • Water’s density at 4°C = 1.00 g/mL

  • If an object is less dense than water, it floats; if more dense, it sinks.

Temperature Scales

  • Celsius (°C) – Used worldwide (0°C freezing, 100°C boiling).

  • Fahrenheit (°F) – Used in the U.S. (32°F freezing, 212°F boiling).

  • Kelvin (K) – Used in science (Absolute zero = 0 K).

Conversion Formulas:

  • C → F: F=(9/5×C)+32F = (9/5 × C) + 32

  • F → C: C=(F−32)×5/9C = (F - 32) × 5/9

  • C → K: K=C+273K = C + 273