1.33333333333 as a fraction

Guri Bee

less than a minute read

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19-10-2024

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Unmasking the Mystery: 1.33333333333 as a Fraction

Have you ever encountered the decimal 1.33333333333 and wondered how to express it as a fraction? This seemingly endless string of threes might seem daunting, but fear not! We'll demystify this number and reveal its hidden fractional form.

Understanding the Repeating Decimal

The key to transforming 1.33333333333 into a fraction lies in recognizing that the decimal portion is a repeating decimal. This means the "3" repeats infinitely. To represent this mathematically, we can use a bar notation, writing it as 1.3̅.

The Conversion Process

1. Set up an equation: Let "x" equal the decimal:

   x = 1.3̅ 
   

2. Multiply to shift the decimal: Multiply both sides of the equation by 10:

   10x = 13.3̅
   

3. Subtract the original equation: Subtract the first equation (x = 1.3̅) from the second equation (10x = 13.3̅):

   10x - x = 13.3̅ - 1.3̅
   9x = 12 
   

4. Solve for x: Divide both sides by 9:

   x = 12/9
   

5. Simplify: Simplify the fraction by dividing both numerator and denominator by their greatest common factor, 3:

   x = 4/3
   

Therefore, 1.33333333333 (or 1.3̅) is equivalent to the fraction 4/3.

Additional Insight:

• This method works for any repeating decimal. You simply need to multiply by a power of 10 that shifts the repeating block to the left of the decimal point.
• The fraction 4/3 is an example of an improper fraction, where the numerator is greater than the denominator. It can also be expressed as a mixed number: 1 1/3.

Practical Applications:

• Baking: Imagine a recipe calls for 1 1/3 cups of flour. You might see this written as 1.33333333333 on a measuring cup. Now you know how to easily convert this decimal back into a fraction.
• Construction: Imagine you need to cut a piece of wood to a length of 1.33333333333 meters. Knowing this is equivalent to 4/3 meters can help you calculate the precise length on your measuring tape.

Remember: Converting repeating decimals to fractions is a valuable skill that can be applied to many different situations. It's a testament to the power of mathematics and its ability to represent complex numbers in different ways.