33.1333 converted to mixed fraction with steps

To convert the decimal 33.1333 into a mixed fraction, follow these steps:

### Step 1: Separate the whole number part
The whole number part of 33.1333 is **33**.

### Step 2: Convert the decimal part to a fraction
The decimal part is 0.1333, which is a repeating decimal.

To convert 0.1333... (with the digit 3 repeating) into a fraction:

#### Step 2.1: Set up an equation to represent the repeating decimal
Let \( x = 0.1333\ldots \)

#### Step 2.2: Eliminate the repeating part
Multiply both sides of the equation by 10 to shift the decimal point one place to the right:

\[
10x = 1.3333\ldots
\]

Now subtract the original equation (\( x = 0.1333\ldots \)) from this new equation:

\[
10x - x = 1.3333\ldots - 0.1333\ldots
\]

This simplifies to:

\[
9x = 1.2
\]

#### Step 2.3: Solve for \( x \)
\[
x = \frac{1.2}{9}
\]

Next, multiply the numerator and the denominator by 10 to eliminate the decimal in the numerator:

\[
x = \frac{12}{90}
\]

Now simplify the fraction \(\frac{12}{90}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 6:

\[
x = \frac{2}{15}
\]

So, 0.1333... as a fraction is \(\frac{2}{15}\).

### Step 3: Combine the whole number with the fraction
Now, combine the whole number part (33) with the fraction part \(\frac{2}{15}\):

\[
33.1333\ldots = 33 \frac{2}{15}
\]

Thus, the mixed fraction form of 33.1333 is **\(33 \frac{2}{15}\)**.

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Would you like more details or have any questions? Here are some related questions:

1. How do you convert 25.6666... to a mixed fraction?
2. What is the process for converting a non-repeating decimal like 5.25 into a mixed fraction?
3. How do you convert a decimal like 0.875 into a fraction and then to a mixed fraction?
4. How can you convert a mixed fraction back to a repeating decimal?
5. What are the steps to simplify a repeating decimal like 0.4444... to a fraction?

**Tip:** When dealing with repeating decimals, it's helpful to represent them algebraically and use subtraction to eliminate the repeating part before simplifying.

Learn how to convert the decimal 33.1333 into a mixed fraction step-by-step. This detailed guide covers separating the whole number part, converting the repeating decimal part to a fraction, and combining them into a mixed fraction. Suitable for students in Grades 7-9 learning decimal conversion and mixed fractions.

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