Write -0.85 as a fraction in simplest form.
The correct answer and explanation is:
✅ Correct Answer:
−0.85=−1720-0.85 = -\dfrac{17}{20}
🧠 Explanation (300 words):
To convert the decimal −0.85-0.85 into a fraction in simplest form, we follow these steps:
🔢 Step 1: Remove the negative sign temporarily
We will deal with the negative sign at the end. So first, convert 0.85 into a fraction.
🔢 Step 2: Convert the decimal into a fraction
Since 0.85 has two decimal places, we can write it as: 0.85=851000.85 = \frac{85}{100}
✂️ Step 3: Simplify the fraction
We need to reduce 85100\frac{85}{100} to its simplest form.
Find the greatest common divisor (GCD) of 85 and 100.
- Factors of 85: 1, 5, 17, 85
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
- GCD of 85 and 100 = 5
Now divide both numerator and denominator by 5: 85÷5100÷5=1720\frac{85 ÷ 5}{100 ÷ 5} = \frac{17}{20}
So, 0.85=17200.85 = \frac{17}{20}
➖ Step 4: Add the negative sign back
Since the original number was -0.85, we just make the fraction negative: −0.85=−1720-0.85 = -\frac{17}{20}
✅ Final Answer:
−0.85=−1720-0.85 = -\frac{17}{20}
🔍 Summary:
- Converting decimals to fractions involves writing the decimal as a fraction with a power of 10 (e.g., 100).
- Then you simplify by dividing the top and bottom by their GCD.
- Finally, you reapply any negative sign.
This method ensures the decimal is expressed as a fraction in its lowest terms, which is the simplest and most accurate fractional representation.