Convert Decimal to Fraction: Express 0.23 in Fractional Form

Q: How do I know what denominator to use?

Count the decimal places (positions after the decimal point). Each place represents a power of 10: 1 place = 10, 2 places = 100, 3 places = 1000, and so on.

Q: Why isn't 0.23 equal to 23/10?

Because $ \frac{23}{10} = 2.3 $, not 0.23! The decimal 0.23 means 23 hundredths, which is $ \frac{23}{100} $.

Q: Do I need to simplify the fraction?

Always check if you can simplify! For $ \frac{23}{100} $, since 23 is prime and doesn't share factors with 100, it's already in lowest terms.

Decimal to Fraction with Place Value

Convert into fraction form:

$0.23=$

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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 between the position of digits after the decimal point to the appropriate division

00:08 Place the digits in the numerator, and the appropriate division in the denominator

00:14 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert into fraction form:

$0.23=$

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

Let's write the fraction in the following way:

$\frac{023}{100}$

Let's then proceed to remove the unnecessary zeros as follows:

$\frac{23}{100}$

Final Answer

$\frac{23}{100}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Count decimal places to determine denominator power
Technique: 0.23 has 2 decimal places, so denominator is $10^2 = 100$
Check: Verify $\frac{23}{100} = 0.23$ by dividing 23 ÷ 100 ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator based on decimal places
Don't count digits instead of decimal places = wrong denominator! 0.23 has 2 digits but that doesn't mean denominator is 10. Always count positions after the decimal point: 2 places means denominator is 100.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

$\frac{5}{100}=$

FAQ

Everything you need to know about this question

How do I know what denominator to use?

Count the decimal places (positions after the decimal point). Each place represents a power of 10: 1 place = 10, 2 places = 100, 3 places = 1000, and so on.

Why isn't 0.23 equal to 23/10?

Because $\frac{23}{10} = 2.3$ , not 0.23! The decimal 0.23 means 23 hundredths, which is $\frac{23}{100}$ .

Do I need to simplify the fraction?

Always check if you can simplify! For $\frac{23}{100}$ , since 23 is prime and doesn't share factors with 100, it's already in lowest terms.

What if the decimal has trailing zeros like 0.230?

Trailing zeros after the decimal don't change the value! 0.230 = 0.23, so you still get $\frac{23}{100}$ . Focus on the significant digits.

How can I double-check my answer?

Divide the numerator by the denominator: 23 ÷ 100 = 0.23. If you get back your original decimal, your fraction is correct!

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