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Convert the decimal under the square root to a fraction.

Biology

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Answer

0.0001

Step-by-step solution

6 steps

  1. Convert the decimal under the square root to a fraction.

    0.00000225=225100,000,0000.00000225 = \frac{225}{100,000,000}

  2. Calculate the square root of the numerator and the denominator separately.

    225=15\sqrt{225} = 15 100,000,000=108=1082=104=10,000\sqrt{100,000,000} = \sqrt{10^8} = 10^{\frac{8}{2}} = 10^4 = 10,000

  3. Substitute these values back into the square root expression.

    0.00000225=225100,000,000=225100,000,000=1510,000\sqrt{0.00000225} = \sqrt{\frac{225}{100,000,000}} = \frac{\sqrt{225}}{\sqrt{100,000,000}} = \frac{15}{10,000}

  4. Substitute this result back into the original problem.

    1510,00015\frac{\frac{15}{10,000}}{15}

  5. Simplify the complex fraction.

    1510,000×115=110,000\frac{15}{10,000} \times \frac{1}{15} = \frac{1}{10,000}

  6. Convert the fraction to a decimal.

    110,000=0.0001\frac{1}{10,000} = 0.0001

    The answer is 0.0001.

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