Convert 0.33 to a Fraction: Step-by-Step Solution

Decimal to Fraction with Place Value

Convert into fraction form:

0.33= 0.33=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Convert to decimal fraction
00:03 Match the position of digits after the decimal point to the appropriate division
00:06 Add 0 to the fraction
00:10 Place the digits in the numerator, and the appropriate division in the denominator
00:15 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Convert into fraction form:

0.33= 0.33=

2

Step-by-step solution

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the zero represents tens

Two numbers after the zero represent hundreds

Three numbers after the zero represent thousands

And so on

In this case, there are two numbers after the zero, so the number is divided by 100

We'll write the fraction in the following way:

033100 \frac{033}{100}

We'll then proceed to remove the unnecessary zeros as follows:

33100 \frac{33}{100}

3

Final Answer

33100 \frac{33}{100}

Key Points to Remember

Essential concepts to master this topic
  • Place Value Rule: Two decimal places means denominator of 100
  • Technique: Write 0.33 as 33100 \frac{33}{100} by counting decimal places
  • Check: Divide 33 ÷ 100 = 0.33 to verify conversion ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring leading zeros in the numerator
    Don't write 033100 \frac{033}{100} in your final answer! Leading zeros don't change the value but look incorrect in simplified form. Always remove unnecessary zeros to write 33100 \frac{33}{100} .

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

\( 0.38= \)

FAQ

Everything you need to know about this question

How do I know what denominator to use?

+

Count the decimal places! One decimal place = 10, two decimal places = 100, three decimal places = 1000. Since 0.33 has two decimal places, use 100 as the denominator.

Do I need to simplify 33100 \frac{33}{100} ?

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Check if 33 and 100 have any common factors. Since 33 = 3 × 11 and 100 = 2² × 5², they share no common factors, so 33100 \frac{33}{100} is already in simplest form!

What's the difference between 0.33 and 0.333...?

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0.33 is exactly thirty-three hundredths, while 0.333... (repeating) equals 13 \frac{1}{3} . The question asks for 0.33, so the answer is 33100 \frac{33}{100} .

Can I write this as a mixed number?

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Since 33100 \frac{33}{100} is less than 1 (33 < 100), it's called a proper fraction and doesn't need to be written as a mixed number. Keep it as 33100 \frac{33}{100} .

How do I check if my fraction equals the original decimal?

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Divide the numerator by the denominator: 33 ÷ 100 = 0.33. If this matches your original decimal, you're correct!

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