Base 10 and Place Value

Base 10 and place value — columns for thousands, hundreds, tens, ones with stacked blocks

Plain English first

We only have 10 digit symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

With just those 10 symbols we can write any number. The trick is place value: the position of a digit determines how much it is worth.

The digit 3 means three. But 300 means three hundreds. And 3000 means three thousands. Same symbol, completely different value depending on where it sits.

The column system

Each column is worth ten times the one to its right:

... | Thousands | Hundreds | Tens | Ones |

The number 4,302 means:

4 thousands  +  3 hundreds  +  0 tens  +  2 ones
= 4000       +  300         +  0       +  2
= 4,302

Standard math notation

N = d₃ × 10³ + d₂ × 10² + d₁ × 10¹ + d₀ × 10⁰

Example: 4302
  = 4 × 1000 + 3 × 100 + 0 × 10 + 2 × 1
  = 4000 + 300 + 0 + 2

Verbose Python with descriptive names

def break_number_into_place_values(whole_number):
    """
    Decompose a number into the value each digit contributes.
    Each column is worth 10× the column to its right — that's base 10.
    """
    column_names = ["ones", "tens", "hundreds", "thousands",
                    "ten-thousands", "hundred-thousands", "millions"]
    breakdown = {}

    for position, digit_character in enumerate(reversed(str(whole_number))):
        digit_value     = int(digit_character)
        column_worth    = 10 ** position
        value_in_column = digit_value * column_worth
        column_label    = column_names[position] if position < len(column_names) else f"10^{position}"
        breakdown[column_label] = {"digit": digit_value, "contributes": value_in_column}

    return breakdown


# Demonstration
breakdown = break_number_into_place_values(4302)
for column, data in breakdown.items():
    print(f"  {column:15s}: digit={data['digit']}, contributes={data['contributes']}")
# Sum confirms: 4000 + 300 + 0 + 2 = 4302

Why base 10?

Probably because humans have 10 fingers. Other bases work identically:
- Base 2 (binary): computers — only digits 0 and 1
- Base 16 (hex): programming — memory addresses, colors (#FF5733)
- Base 60: ancient Babylonians — why we have 60 minutes and 60 seconds

Common mistakes

The digit 4 in 4,302 is worth 4,000 — not 4.
Dropping placeholder zeros. 4,302 ≠ 432.
Thinking "ones" means unimportant. Everything is built in multiples of the ones column.

Resultados