Which statement about 0.374̅9, 0.375, and 3/8 is correct?
Answer and explanation
Correct answer: 0.374̅9 = 0.375 = 3/8
The bar over 9 means that 9 repeats: 0.3749999… This value is equal to 0.375 because 0.375 − 0.3749999… is zero in the limiting decimal sense; equivalently, 0.374999… = 0.375. Also, 3/8 can be converted directly to a decimal: 3 ÷ 8 = 0.375. Therefore all three expressions have the same value, so option C is correct. Option A incorrectly treats the repeating-9 decimal as slightly smaller, and options B and D incorrectly impose an inequality. A repeating 9 can complete the next terminating decimal value.
Frequently asked questions
What is the correct answer to this question?
0.374̅9 = 0.375 = 3/8
Why is this the correct answer?
The bar over 9 means that 9 repeats: 0.3749999… This value is equal to 0.375 because 0.375 − 0.3749999… is zero in the limiting decimal sense; equivalently, 0.374999… = 0.375. Also, 3/8 can be converted directly to a decimal: 3 ÷ 8 = 0.375. Therefore all three expressions have the same value, so option C is correct. Option A incorrectly treats the repeating-9 decimal as slightly smaller, and options B and D incorrectly impose an inequality. A repeating 9 can complete the next terminating decimal value.
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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