NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - True or False Questions
Question 62

Question. 62

Of two natural numbers, the one having more digits is greater.

Answer:

true

Detailed Answer with Explanation:

Step 1: Natural numbers do not have leading zeros. So a number like 007 is not allowed; it is just 7.

Step 2: If a number has k digits, the smallest such number is \(10^{k-1}\).

For example, for 3 digits the smallest is \(10^{3-1} = 10^2 = 100\).

Step 3: All k-digit numbers are less than \(10^k\).

For example, all 3-digit numbers are \(< 10^3 = 1000\), so the greatest 3-digit number is 999.

Step 4: Any number with k+1 digits is at least \(10^k\).

Step 5: Compare ranges:

\(\text{k-digit numbers} < 10^k\) and \(\text{(k+1)-digit numbers} \ge 10^k\).

This shows every (k+1)-digit number is bigger than every k-digit number.

Conclusion: More digits ⇒ larger number. Therefore, the statement is true.

NCERT Exemplar Solutions Class 6 – Mathematics – Unit 1: Number System – True or False Questions | Detailed Answers