Write -12.405 as a mixed number in simplest form.

Write -12.405 as a mixed number in simplest form.

The Correct Answer and Explanation is:

Correct Answer:
−12.405-12.405 as a mixed number in simplest form is: −1281200-12 \dfrac{81}{200}

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Explanation
To convert −12.405-12.405 into a mixed number in simplest form, we follow these steps:

1. Separate the Whole Number and Decimal

−12.405-12.405 has a whole number part −12-12 and a decimal part 0.4050.405.

2. Convert the Decimal to a Fraction

We now convert 0.4050.405 into a fraction. 0.405=40510000.405 = \frac{405}{1000}

We use 1000 as the denominator because there are three digits after the decimal point.

3. Simplify the Fraction

Now, simplify 4051000\frac{405}{1000} by finding the greatest common divisor (GCD) of 405 and 1000.

Factors of 405:
405 = 5 × 81 = 5 × 3 × 3 × 3 × 3
= 5×345 \times 3^4

Factors of 1000:
1000 = 23×532^3 \times 5^3

The common factor is 5. 405÷51000÷5=81200\frac{405 \div 5}{1000 \div 5} = \frac{81}{200}

So, 0.405=812000.405 = \frac{81}{200}

4. Write as a Mixed Number

Now combine the whole number and the simplified fraction: −12.405=−1281200-12.405 = -12 \frac{81}{200}

5. Final Answer

Thus, −12.405-12.405 written as a mixed number in simplest form is: −1281200\boxed{-12 \frac{81}{200}}

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Why This Matters:

Writing decimals as mixed numbers is helpful in contexts like cooking, measurements, and fractions in algebra. This process reinforces understanding of place value, simplification, and number conversion. Always ensure the final fraction is in simplest form, and if the decimal is negative, the whole mixed number retains that negative sign.