Place value and face value — how to read and write large numbers

Question

In the number 5,83,47,921 — what is the place value and face value of the digit 8? How do we read this number in the Indian system and the International system?

(CBSE 6 Board pattern)

Solution — Step by Step

flowchart TD
    A["Given a large number"] --> B["Identify each digit's position"]
    B --> C["Face Value = the digit itself"]
    B --> D["Place Value = digit × position value"]
    A --> E{"Which number system?"}
    E -- Indian --> F["Group: Ones, Thousands, Lakhs, Crores"]
    E -- International --> G["Group: Ones, Thousands, Millions, Billions"]
    F --> H["Use commas after 3 digits, then every 2"]
    G --> I["Use commas every 3 digits from right"]

Why This Works

Our number system is positional — the same digit means different things in different positions. The digit 5 in the ones place means 5, but in the crores place it means 5,00,00,000. Face value ignores position, while place value accounts for it. This is the foundation of how we write any number using just 10 digits (0-9).

The Indian and International systems differ only in how they group digits for reading convenience. The mathematical value of the number is identical.

Alternative Method

To quickly find the place value of any digit, count positions from the right (starting at 0):

Position 0 = ones ($10^0 = 1$), Position 1 = tens ($10^1 = 10$), Position 2 = hundreds ($10^2 = 100$), and so on.

Place value of digit $d$ at position $p$ = $d \times 10^p$.

Common Mistake