Which decimal is greater than 0.4 but less than 0.5?
Answer and explanation
Correct answer: 0.405
The governing idea is comparison of decimals using place value and equivalent notation. Express the boundaries as 0.400 and 0.500 so that all relevant places can be compared. The number 0.405 has the same whole-number and tenths digits as the lower boundary, but its thousandths digit makes it slightly larger than 0.400. It is still less than 0.500, so 0.400 < 0.405 < 0.500. Hence option B is correct. The value 0.39 is below 0.4, while 0.50 is exactly equal to the upper boundary and therefore is not strictly less than 0.5. The value 0.504 is greater than 0.5. Writing a trailing zero in 0.4 and 0.5 does not alter their values; it simply allows a fair digit-by-digit comparison.
Frequently asked questions
What is the correct answer to this question?
0.405
Why is this the correct answer?
The governing idea is comparison of decimals using place value and equivalent notation. Express the boundaries as 0.400 and 0.500 so that all relevant places can be compared. The number 0.405 has the same whole-number and tenths digits as the lower boundary, but its thousandths digit makes it slightly larger than 0.400. It is still less than 0.500, so 0.400 < 0.405 < 0.500. Hence option B is correct. The value 0.39 is below 0.4, while 0.50 is exactly equal to the upper boundary and therefore is not strictly less than 0.5. The value 0.504 is greater than 0.5. Writing a trailing zero in 0.4 and 0.5 does not alter their values; it simply allows a fair digit-by-digit comparison.
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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