Smallest Rational Number to Be Multiplied with 1/3 for One Decimal Place

Video Explanation

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Solution

Question: The smallest rational number by which 1/3 should be multiplied so that its decimal expansion terminates after one place of decimal.

Step 1: Requirement for One Decimal Place

A decimal that terminates after one decimal place must be of the form:

= some integer / 10

Step 2: Assume the Product

Let the required rational number be x.

Then:

(1/3) × x = 1/10

Step 3: Find the Value of x

x = (1/10) × 3

x = 3/10

Step 4: Check

(1/3) × (3/10) = 1/10 = 0.1

The decimal expansion terminates after one decimal place.

Final Answer

✔ The smallest rational number is 3/10.

Conclusion

Thus, multiplying 1/3 by 3/10 gives 0.1, which terminates after one decimal place.