Rewrite as a simplified fraction 3.1 (3 repeating)
Normally, fractions are not written having decimal numbers in the numerator and denominator. So, while 14.1/4.5 is in fact a correct value, it is not acceptable as a simplified fraction.
We all know that 0.33333... = 1/3
so, 3.133333... = 3 1/10 + 1/30 = 3 2/15 = 47/15
Sorry for the mistake. You are correct.
The fraction 3.1 (3 repeating) can be simplified to 47/15.
To rewrite 3.1 (3 repeating) as a simplified fraction, we can use the concept of repeating decimals.
Let x = 3.1 (3 repeating).
To get rid of the repeating decimal, we can multiply both sides of the equation by 10, which moves the decimal point one place to the right:
10x = 31.3 (3 repeating).
Now, we can subtract the original equation (x = 3.1 (3 repeating)) from this new equation (10x = 31.3 (3 repeating)):
10x - x = 31.3 (3 repeating) - 3.1 (3 repeating).
Simplifying the equation, we have:
9x = 28.2.
To isolate x, we divide both sides of the equation by 9:
x = 28.2 / 9 = 3.133 (repeating).
Therefore, 3.1 (3 repeating) can be simplified as the fraction 3.133 (repeating) / 1.
To rewrite 3.1 (3 repeating) as a simplified fraction, we can use the concept of recurring decimals.
Let x = 3.1 (3 repeating).
To eliminate the repeating decimal, we can multiply both sides of the equation by 10, so 10x = 31.3 (3 repeating).
Now, we can subtract the original equation from the new equation to eliminate the repeating decimal:
(10x - x) = (31.3 (3 repeating) - 3.1 (3 repeating))
Simplifying further, we have:
9x = 28.2
Now we can solve for x by dividing both sides of the equation by 9:
9x/9 = 28.2/9
x = 3.133333...
To express x as a simplified fraction, we can make use of the fact that x = 3.133333...
Let's define another variable y = 3.133333...
Now, subtracting y from x, we have:
x - y = 3.133333... - 3.133333...
Simplifying further, we get:
0 = 0
This means that x - y = 0, which implies that x = y.
So, we can say that x = 3.133333... is equal to y.
To express y as a simplified fraction, we need to consider that the decimal part of y (0.133333...) is a repeating decimal.
Since there is only one digit repeating, we can represent it as a fraction with a single digit repeating in the numerator and 9 repeating in the denominator.
Therefore, y can be expressed as the simplified fraction:
y = 1/9
Hence, we can conclude that 3.1 (3 repeating) written as a simplified fraction is 3 1/9.
To rewrite 3.1 (3 repeating) as a simplified fraction, we can let x = 3.1 (3 repeating):
x = 3.133333...
Multiplying both sides by 10 to eliminate the repeating decimal, we get:
10x = 31.333333...
Subtracting the equation x from 10x, we have:
10x - x = 31.333333... - 3.133333...
9x = 28.2
To simplify the fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 9:
x = 28.2/9 = 14.1/4.5
Therefore, 3.1 (3 repeating) can be simplified to 14.1/4.5.