-1.3125 as a fraction in simplest form

-1.3125 as a fraction in simplest form

The Correct Answer and Explanation is:

To convert the decimal -1.3125 to a fraction in simplest form, let’s follow a step-by-step approach.

Step 1: Understand the decimal place value

The decimal -1.3125 has four digits after the decimal point. This means it can be expressed as:

[
-1.3125 = -\frac{13125}{10000}
]

Step 2: Simplify the fraction

To simplify this fraction, we need to find the greatest common divisor (GCD) of the numerator (13125) and the denominator (10000). The GCD of 13125 and 10000 is 125.

Step 3: Divide both the numerator and denominator by the GCD

Now, divide both the numerator and the denominator by their GCD, which is 125:

[
\frac{13125 \div 125}{10000 \div 125} = \frac{105}{80}
]

Step 4: Simplify further

The fraction (\frac{105}{80}) can be simplified further. The GCD of 105 and 80 is 5, so we divide both the numerator and denominator by 5:

[
\frac{105 \div 5}{80 \div 5} = \frac{21}{16}
]

Final Answer:

Thus, the decimal -1.3125 as a fraction in simplest form is:

[
-1.3125 = -\frac{21}{16}
]

Explanation:

1. We begin by expressing the decimal -1.3125 as a fraction: (-\frac{13125}{10000}).
2. The next step is to simplify the fraction. This involves finding the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 13125 and 10000 is 125.
3. Dividing both the numerator and the denominator by 125 simplifies the fraction to (\frac{105}{80}).
4. The final simplification comes by dividing both 105 and 80 by their GCD, which is 5, yielding the fraction (\frac{21}{16}).
5. Since the original decimal was negative, the final fraction is negative as well: (-\frac{21}{16}).

This is the simplest form of the fraction representation for the decimal -1.3125.