What is 1.3333 (repeating 3) as a fraction? How to convert it?

What is 1.3333 as a fraction? How to convert 1.3333 into a fraction? Through the decimal to fraction calculator, we can get the answer of 1.3333 to a fraction is 43, expressed as a mixed fraction is 113. Here are two ways to change 1.3333 into a fraction.

Through the decimal to fraction calculator page, we know that there are four steps to convert decimals into fractions:

So, following these 4 steps, we will complete it step by step.

Step 1. Convert the decimal to an integer equation.

1.3333, the decimal point is followed by 3 non-recurring decimal places of 333, and then followed by a repeating trailing decimal place of 3. Let x = 1.3333, then 1000x = 1333.3, 10000x = 13333.3.

10000x – 1000x = 13333.3 – 1333.3
9000x = 12000

Step 2. Convert integer equations into a fraction.

The equation got from Step 1, divide both sides by 9000 at the same time to get the initial fraction form.

x = 120009000
1.3333 = 120009000

Step 3. Find the greatest common divisor.

Next, we have to find the greatest common divisor of 12000 and 9000.

The factors of 12000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 75, 80, 96, 100, 120, 125, 150, 160, 200, 240, 250, 300, 375, 400, 480, 500, 600, 750, 800, 1000, 1200, 1500, 2000, 2400, 3000, 4000, 6000, 12000.

The factors of 9000 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 125, 150, 180, 200, 225, 250, 300, 360, 375, 450, 500, 600, 750, 900, 1000, 1125, 1500, 1800, 2250, 3000, 4500, 9000.

So, the greatest common divisor of 12000 and 9000 is 3000.

GCD(12000, 9000) = 3000

Step 4. Simplify the fraction

Now, we have found that the greatest common divisor of 12000 and 9000 is 3000. Therefore, the numerator and denominator of the initial fraction are divided by 3000 to get the final simplified fraction.

1.3333 = 120009000
= 12000 ÷ 30009000 ÷ 3000
= 43
= 113

So, the answer of 1.3333 as a fraction is 43, expressed as a mixed fraction is 113.

This is the routine conversion process from decimal to fraction. Is there a simpler one? Let’s take a look at the following method.

Obviously, 1.3333 is an infinite recurring decimal, there are non-recurring decimals and recurring decimals after the decimal point. The length of the non-recurring decimal places is 3, and the length of the trailing decimal places to be repeated is 1. Through the infinite recurring decimal to fraction formula, we can get that the initial denominator of the fraction is 9000 and the initial numerator is 13333 – 1333 = 12000. So the initial form of the fraction is 120009000.

The next steps are the same as Method 1. Find the greatest common divisor of 12000 and 9000 is 3000, then simplify the initial fraction. The final answer is also 43.

Comparing these two methods, both methods can calculate the fraction of 1.3333, but the second formula method is relatively simple and can get the initial form of the fraction in one step.

Finally, tell you a little trick which can save all the calculation steps. This is directly using the online free decimal to fraction calculator we provide. Both finite and infinite decimals can be easily converted to fractions. Of course, the final fraction is simplified. It can be an improper fraction or a mixed fraction. Everyone is welcome to use!