Large Numbers Around Us | A

Question 1

Calculate the product to uncover the fact. Once you find the product, read the number in both Indian and American naming systems. Share your thoughts and questions about the fact with the class after you discover each number.

Solution

Understand the Question

To multiply large numbers ending in zeros, separate the non-zero parts from powers of $10$ , multiply the base numbers, and then append the total count of zeros.
Indian Naming System: Commas are placed after the first $3$ digits from the right (hundreds), and then after every $2$ digits (thousands, lakhs, crores).
American (International) System: Commas are placed after every $3$ digits from the right (thousands, millions, billions).

Step 1 · Calculate the Product

Given expression $6400 \times 62,500$ Diagram 1

Rewrite by factoring out powers of $10$

\begin{aligned} 6400 \times 62,500 &= (64 \times 100) \times (625 \times 100) \\[0.6em] &= (64 \times 625) \times (100 \times 100) \\[0.6em] &= 40,000 \times 10,000 \\[0.6em] &= 400,000,000 \end{aligned}

Step 2 · Read in the Indian System

In the Indian numbering system, group digits in periods of $3$ , then $2$ , $2$ , and so on from the right $40,00,00,000$

In words $\text{Forty Crore}$

Step 3 · Read in the American System

In the American (International) numbering system, group digits in periods of $3$ from the right $400,000,000$

In words $\text{Four Hundred Million}$

Step 4 · Reflect on the Fact

The Amazon river discharges $400,000,000\text{ litres}$ of water every second. This enormous freshwater flow pushes far into the Atlantic Ocean, illustrating the massive scale of the river's drainage basin.

Answer

Product: $400,000,000$

Indian System: Forty Crore ( $40,00,00,000$ )
American System: Four Hundred Million ( $400,000,000$ )

Common Mistakes

Zero Counting Error: Forgetting the zero generated by the product $64 \times 625 = 40,000$ , which gives $4$ zeros before multiplying by $10,000$ (total $8$ zeros, yielding $400,000,000$ ).
Period Grouping: Confusing the Indian grouping ( $40,00,00,000$ ) with the American grouping ( $400,000,000$ ).

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