1.66666666667 as a fraction

Lyra Rowan

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29-09-2024

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Unmasking the Mystery: 1.66666666667 as a Fraction

Have you ever encountered the decimal 1.66666666667 and wondered how to represent it as a fraction? It might seem daunting at first, but with a little understanding of decimals and fractions, we can easily crack this code. Let's dive in!

Understanding the Repeating Decimal

First, we need to recognize that 1.66666666667 is a repeating decimal. The "6" repeats infinitely. This repetition is key to converting it into a fraction.

The Steps

Let's break down the process:

1. Assign a Variable: Let 'x' equal the decimal 1.66666666667. So, x = 1.66666666667.

2. Multiply to Shift the Decimal: Multiply both sides of the equation by 10. This moves the decimal one place to the right. We now have 10x = 16.6666666667.

3. Subtract the Original Equation: Subtract the original equation (x = 1.66666666667) from the new equation (10x = 16.6666666667). This eliminates the repeating decimal portion:

   10x = 16.6666666667
   - x =  1.6666666667
   ------------------
   9x = 15 
   

4. Solve for x: Divide both sides by 9 to isolate 'x'. This gives us x = 15/9.

5. Simplify: The fraction 15/9 can be simplified by dividing both the numerator and denominator by their greatest common factor, 3. This results in the simplified fraction 5/3.

Therefore, 1.66666666667 is equivalent to the fraction 5/3.

A Real-World Example

Imagine you're splitting a pizza into three equal slices. You eat two of those slices. You've consumed 2/3 of the pizza. This is equivalent to 0.66666666667.

Additional Considerations

• While we used a decimal approximation for this example, remember that the "6" repeats infinitely. This means the fraction 5/3 is the exact representation.

• This method can be applied to any repeating decimal, just adjust the multiplication factor to shift the decimal to the appropriate position.

Credits:

While this article provides an explanation of the process, the initial question about converting 1.66666666667 to a fraction was originally posed on Brainly. This exploration builds upon the collective knowledge shared on the platform.