What is the decimal form of 201(25/100000)?

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What is the decimal form of 201(25/100000)?

  1. A.

    201.00026

  2. B.

    202.00025

  3. C.

    201.000025

  4. D.

    201.00025

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Show answer & explanation

Correct answer: D

To convert a mixed number of the form whole number + fraction into decimal form, convert the fractional part to a decimal and add it to the whole number. When the fraction's denominator is a power of 10 (10, 100, 1000, ...), the number of zeros in the denominator equals the number of digits that appear after the decimal point in the fraction's decimal form.

  1. Split 201(25/100000) into its whole-number part, 201, and its fractional part, 25/100000.

  2. Count the zeros in the denominator 100000 - there are five zeros, so the fraction occupies five digits after the decimal point.

  3. Write the numerator 25 into those five decimal places: 25/100000 = 0.00025.

  4. Add the fractional decimal to the whole number: 201 + 0.00025 = 201.00025.

Check by reversing the conversion: 201.00025 x 100000 = 20100025, and 201 x 100000 + 25 = 20100000 + 25 = 20100025 - the two match, confirming 201.00025 is the correct decimal form.

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