Convert Decimal 0.09: Finding All Equivalent Forms

Q: Why is 0.09 equal to 9/100 and not 09/100?

Leading zeros don't affect the value! $ \frac{009}{100} $ and $ \frac{9}{100} $ are mathematically identical, but we always simplify by removing unnecessary zeros.

Q: How do I remember which denominator to use?

Count the decimal places! One place = tenths (÷10), two places = hundredths (÷100), three places = thousandths (÷1000). For 0.09, there are 2 decimal places, so use 100.

Q: How can I double-check my answer?

Divide your fraction: $ \frac{9}{100} = 9 ÷ 100 = 0.09 $ ✓. If you get back to your original decimal, you're correct!

Decimal Conversion with Place Value Recognition

Convert into fraction form:

$0.09=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's convert this number to a decimal fraction.

00:09 Ensure each digit after the decimal point matches with its correct division.

00:15 Write these digits in the numerator, and place the correct division number in the denominator.

00:21 And that's how we solve this question. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert into fraction form:

$0.09=$

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:

$\frac{009}{100}$

We'll then remove the unnecessary zeros as follows:

$\frac{9}{100}$

Final Answer

$\frac{9}{100}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Two digits after decimal point means divide by 100
Technique: Write 0.09 as 9/100, keeping the 9 in numerator
Check: Divide 9 ÷ 100 = 0.09 to verify your fraction ✓

Common Mistakes

Avoid these frequent errors

Including zeros in the numerator
Don't write 0.09 as 009/100 or 090/100 = incorrect fractions! Leading zeros don't change the value but create confusion. Always use just the significant digits: write 0.09 as 9/100.

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

Why is 0.09 equal to 9/100 and not 09/100?

Leading zeros don't affect the value! $\frac{009}{100}$ and $\frac{9}{100}$ are mathematically identical, but we always simplify by removing unnecessary zeros.

How do I remember which denominator to use?

Count the decimal places! One place = tenths (÷10), two places = hundredths (÷100), three places = thousandths (÷1000). For 0.09, there are 2 decimal places, so use 100.

Can I simplify 9/100 further?

Let's check: 9 = 3 × 3 and 100 = 4 × 25. Since 9 and 100 share no common factors, $\frac{9}{100}$ is already in its simplest form!

What if I wrote 90/1000 instead?

That's incorrect! 90/1000 = 0.090 = 0.09, but you're making it unnecessarily complex. Always use the smallest denominator possible based on decimal places: 0.09 has 2 places, so use 100.

How can I double-check my answer?

Divide your fraction: $\frac{9}{100} = 9 ÷ 100 = 0.09$ ✓. If you get back to your original decimal, you're correct!

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