Convert 1.16666666667 to a fraction.

Convert 1.16666666667 to a fraction.

The Correct Answer and Explanation is:

To convert the decimal (1.16666666667) into a fraction, we start by separating the whole number part from the decimal part. The whole number part is (1), and the decimal part is (0.16666666667).

Step 1: Converting the Decimal Part

The decimal (0.16666666667) is a repeating decimal, where the digit (6) repeats indefinitely. This can be represented as (0.16\overline{6}).

Step 2: Setting Up the Equation

Let (x = 0.16666666667).

To eliminate the repeating part, we can multiply (x) by (10) (to shift the decimal point one place to the right):
[
10x = 1.66666666667
]
Now we have two equations:

1. (x = 0.16666666667)
2. (10x = 1.66666666667)

Step 3: Subtracting the Equations

Next, we subtract the first equation from the second:
[
10x – x = 1.66666666667 – 0.16666666667
]
This simplifies to:
[
9x = 1.5
]

Step 4: Solving for (x)

Now, we can solve for (x) by dividing both sides by (9):
[
x = \frac{1.5}{9}
]
To simplify (\frac{1.5}{9}), we can multiply the numerator and the denominator by (10) to eliminate the decimal:
[
x = \frac{15}{90}
]
Now, we simplify (\frac{15}{90}):
[
x = \frac{1}{6}
]

Step 5: Combining with the Whole Number

Now that we have the fractional part, we can combine it with the whole number part:
[
1 + \frac{1}{6} = \frac{6}{6} + \frac{1}{6} = \frac{7}{6}
]

Final Result

Thus, the decimal (1.16666666667) can be expressed as the fraction (\frac{7}{6}).

In conclusion, converting repeating decimals to fractions involves recognizing the repeating pattern, setting up an equation, eliminating the repeating part through subtraction, and finally simplifying the result. This process reveals that (1.16666666667) is equivalent to the fraction (\frac{7}{6}), which can also be expressed as an improper fraction, indicating that it is slightly more than (1).