1.333333333333333 as a simplified fraction
The Correct Answer and Explanation is :
The number (1.333333333333333) can be expressed as a simplified fraction. To do this, we first recognize that the repeating decimal (1.333…) can be rewritten as:
[
1.333… = 1 + 0.333…
]
Next, we need to convert the repeating decimal (0.333…) into a fraction. Let’s denote (x = 0.333…).
To eliminate the repeating decimal, we can multiply both sides of this equation by 10:
[
10x = 3.333…
]
Now, we have two equations:
- (x = 0.333…)
- (10x = 3.333…)
Next, we can subtract the first equation from the second:
[
10x – x = 3.333… – 0.333…
]
This simplifies to:
[
9x = 3
]
Dividing both sides by 9 gives:
[
x = \frac{3}{9}
]
We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3:
[
x = \frac{1}{3}
]
Now that we have (0.333… = \frac{1}{3}), we can substitute this back into our earlier expression for (1.333…):
[
1.333… = 1 + 0.333… = 1 + \frac{1}{3}
]
To combine these, we express (1) as a fraction with the same denominator as (\frac{1}{3}):
[
1 = \frac{3}{3}
]
Now, we can add the two fractions:
[
1.333… = \frac{3}{3} + \frac{1}{3} = \frac{3 + 1}{3} = \frac{4}{3}
]
Thus, the decimal (1.333333333333333) can be expressed as the simplified fraction (\frac{4}{3}).
In summary, by recognizing the repeating decimal, converting it into a fraction, and performing basic arithmetic operations, we arrive at the simplified fraction representation of the original decimal.