What is 12.8 converted to a fraction? the answer should be given in simplest form.
The Correct Answer and Explanation is :
To convert the decimal 12.8 to a fraction in its simplest form, follow these steps:
Step 1: Understand the Decimal
The number 12.8 consists of a whole number part (12) and a decimal part (0.8). We can express 12.8 as:
[
12.8 = 12 + 0.8
]
Step 2: Convert the Decimal Part to a Fraction
Next, we focus on converting 0.8 into a fraction. The decimal 0.8 can be represented as:
[
0.8 = \frac{8}{10}
]
This fraction comes from the fact that the digit 8 is in the tenths place.
Step 3: Simplify the Fraction
Now, we simplify (\frac{8}{10}). Both the numerator and the denominator can be divided by their greatest common divisor (GCD), which is 2:
[
\frac{8 \div 2}{10 \div 2} = \frac{4}{5}
]
So, (0.8) can be expressed as the simplified fraction (\frac{4}{5}).
Step 4: Combine the Whole Number and Fraction
Now we can combine the whole number (12) with the fraction (\frac{4}{5}). This gives us:
[
12.8 = 12 + 0.8 = 12 + \frac{4}{5}
]
To express this as a single fraction, we convert 12 into a fraction with the same denominator (5):
[
12 = \frac{12 \times 5}{5} = \frac{60}{5}
]
Step 5: Add the Fractions
Now, we can add the two fractions:
[
\frac{60}{5} + \frac{4}{5} = \frac{60 + 4}{5} = \frac{64}{5}
]
Step 6: Final Answer
Thus, 12.8 converted to a fraction in simplest form is:
[
\frac{64}{5}
]
This fraction cannot be simplified further, as 64 and 5 have no common factors other than 1.
Summary
In summary, to convert the decimal 12.8 to a fraction, we separate the whole number and the decimal part, convert the decimal part into a fraction, simplify it, and then combine both parts to arrive at the final answer of (\frac{64}{5}).