If (0.5a9<0.549), what can be the greatest value of digit (a)?
Answer and explanation
Correct answer: (3)
Compare 0.5a9 and 0.549 by examining their decimal places from left to right. The digits in the tenths place are both 5, so that place does not decide the comparison. In the hundredths place, the first number has a and the second number has 4. For 0.5a9 to be less than 0.549, a must be less than 4. The greatest digit satisfying this condition is 3.
With a equal to 3, the numbers are 0.539 and 0.549, and 0.539 is indeed smaller. If a were 4, the numbers would be 0.549 and 0.549, giving equality rather than a strict less-than relation. Any digit above 4 would make the first number larger. Hence the greatest possible value is 3, which is option B.
Frequently asked questions
What is the correct answer to this question?
(3)
Why is this the correct answer?
Compare 0.5a9 and 0.549 by examining their decimal places from left to right. The digits in the tenths place are both 5, so that place does not decide the comparison. In the hundredths place, the first number has a and the second number has 4. For 0.5a9 to be less than 0.549, a must be less than 4. The greatest digit satisfying this condition is 3.
With a equal to 3, the numbers are 0.539 and 0.549, and 0.539 is indeed smaller. If a were 4, the numbers would be 0.549 and 0.549, giving equality rather than a strict less-than relation. Any digit above 4 would make the first number larger. Hence the greatest possible value is 3, which is option B.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Decimal representation.
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