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Numbers & Counting

Mathematics is the universal language of quantity, pattern, and logic. Unlike spoken language, math works the same way everywhere on Earth. Numbers transcend borders.

The Number System

Humans primarily use the decimal (base-10) system — ten digits that combine to represent any quantity:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

When you run out of single digits, you add places:

  • 10 = “ten”
  • 100 = “one hundred”
  • 1,000 = “one thousand”
  • 1,000,000 = “one million”
  • 1,000,000,000 = “one billion”

The system is positional — the value of a digit depends on its position. In 3,472:

  • The 3 represents 3,000
  • The 4 represents 400
  • The 7 represents 70
  • The 2 represents 2

Counting

Counting is assigning numbers to objects in sequence. Starting at zero (or one), each object gets the next number.

Ordinal numbers tell position: first, second, third, fourth… (1st, 2nd, 3rd, 4th…)

Negative Numbers

Numbers can go below zero. Negative numbers (represented with a minus sign -) are useful for:

  • Temperature below freezing (e.g., -10°C)
  • Debt (owing money)
  • Elevation below sea level

The number line looks like this:

...-4  -3  -2  -1  0  1  2  3  4...

Fractions and Decimals

Not everything is a whole number.

Fractions represent parts of a whole:

  • 1/2 = one half (split something into 2, take 1)
  • 3/4 = three quarters (split into 4, take 3)
  • 1/4 = one quarter

Decimals express the same thing differently:

  • 1/2 = 0.5
  • 3/4 = 0.75
  • 1/4 = 0.25

The . (decimal point) separates whole numbers from fractions.

Percentages (%) express fractions of 100:

  • 50% = half = 0.5
  • 25% = one quarter = 0.25
  • 100% = the whole thing

Zero

Zero (0) is a profound concept that took humans a surprisingly long time to formalize. It represents the absence of quantity. It is neither positive nor negative. Multiplying anything by zero gives zero. Dividing by zero is undefined (mathematically problematic).

Why Numbers Matter in Daily Life

  • Time — hours, minutes, seconds (A Typical Day)
  • Money — prices, wages, budgets (Economics & Money)
  • Measurement — distance, weight, volume
  • Dates — calendars
  • Quantities — cooking, shopping, counting anything

Related: Basic Arithmetic | Money & Measurement | Why Math Matters Next: Basic Arithmetic