What is obtained when (0.0003125) is converted into a simplified fraction?
Answer and explanation
Correct answer: 1/3200
The governing concept is the conversion of a terminating decimal into a fraction with a power of 10 as denominator, followed by reduction to lowest terms. The decimal 0.0003125 has seven digits after the decimal point, so it is 3125/10,000,000. Now divide numerator and denominator by 3125, their greatest common divisor: 3125 ÷ 3125 = 1 and 10,000,000 ÷ 3125 = 3200. Hence 0.0003125 = 1/3200, making option B correct. Option D is the unreduced fraction and is also written with an incorrect denominator for seven decimal places; 1/320 and 1/32000 have values ten times larger and ten times smaller, respectively. The simplified fraction must have numerator 1 and denominator 3200.
Frequently asked questions
What is the correct answer to this question?
1/3200
Why is this the correct answer?
The governing concept is the conversion of a terminating decimal into a fraction with a power of 10 as denominator, followed by reduction to lowest terms. The decimal 0.0003125 has seven digits after the decimal point, so it is 3125/10,000,000. Now divide numerator and denominator by 3125, their greatest common divisor: 3125 ÷ 3125 = 1 and 10,000,000 ÷ 3125 = 3200. Hence 0.0003125 = 1/3200, making option B correct. Option D is the unreduced fraction and is also written with an incorrect denominator for seven decimal places; 1/320 and 1/32000 have values ten times larger and ten times smaller, respectively. The simplified fraction must have numerator 1 and denominator 3200.
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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