As you did before, divide the given numbers to uncover interesting facts about division. Share your thoughts and questions with the class after you uncover each number.

Question

Homi · Accepted Answer

Understand the Question

To uncover the fact, divide the large numbers given in the problem: $13,95,000 \div 150$ .
Simplify the division by canceling common factors of $10$ , perform long division, and attach the remaining zeros to find the total distance.

Step 1 · Calculate the Journey Distance

Diagram 1

Simplify the division by dividing both numbers by $10$ $13,95,000 \div 150 = 139,500 \div 15$

Dividing $1395$ by $15$

\begin{aligned} 139 \div 15 &= 9 \quad (\text{Remainder } 4) \\ 45 \div 15 &= 3 \quad (\text{Remainder } 0) \end{aligned}

So, $1395 \div 15 = 93$ .

Attaching the two remaining zeros from $139,500$ $139,500 \div 15 = 9300$

$\text{Distance} = 9300 \text{ km}$

Step 2 · Interpret the Result

The distance of the longest single-train journey in the world (Moscow to Vladivostok) is $9300\text{ km}$ , taking about $7$ days.
For comparison, India's longest train route (Dibrugarh to Kanyakumari) is $4219\text{ km}$ (takes about $76$ hours).

Answer

The distance of the longest single-train journey in the world is $9300\text{ km}$ .

Common Mistakes

Zero Omission: Forgetting to add back the remaining two zeros to $93$ after dividing $1395 \div 15$ , leading to an answer of $93\text{ km}$ instead of $9300\text{ km}$ .
Simplification Error: Incorrectly canceling zeros (e.g., canceling two zeros from the dividend when the divisor only has one zero).

Question 2

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