Convert 0.0008 to Its Simplified Fraction Form

Q: How do I know what denominator to use?

Count the decimal places in your number. Each place represents a power of 10: 1 place = 10, 2 places = 100, 3 places = 1000, 4 places = 10000, and so on.

Q: Why isn't 8/1000 the right answer for 0.0008?

8/1000 = 0.008, which is different from 0.0008! The extra zero in 0.0008 means it's in the ten-thousandths place, not thousandths.

Q: What if the decimal has zeros in the middle?

Count all decimal places, including zeros! For example, 0.0508 has 4 decimal places, so it becomes $ \frac{508}{10000} $.

Decimal to Fraction with Place Value

Convert 0.0008 into a fraction.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's turn this into a simple fraction.

00:07 First, move the decimal point to the right until it's a whole number.

00:12 Remember, in a decimal fraction, the bottom number needs to be a ten, or a multiple of ten.

00:18 Move the decimal point four spaces to the right.

00:22 Now, add four zeros to that denominator.

00:27 Put all the digits up top here, in the numerator.

00:38 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert 0.0008 into a fraction.

Step-by-step solution

To convert 0.0008 into a fraction, follow these steps:

Step 1: Identify the number of decimal places in 0.0008. The number 0.0008 is equal to 8 thousandths.

Step 2: Write 0.0008 as a fraction. Since there are four decimal places in 0.0008, you can express it as:

$0.0008 = \frac{8}{10000}$

Step 3: Simplify the fraction if applicable. In this case, the fraction $\frac{8}{10000}$ is already in its simplest form, as there are no common factors between 8 and 10000 apart from 1.

Therefore, the fraction representation of the decimal 0.0008 is $\frac{8}{10000}$ .

Final Answer

$\frac{8}{10000}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Count decimal places to determine denominator power of 10
Technique: 0.0008 has 4 decimal places, so $\frac{8}{10000}$
Check: Divide 8 ÷ 10000 = 0.0008 to verify conversion ✓

Common Mistakes

Avoid these frequent errors

Miscounting decimal places
Don't count just the non-zero digits or stop at the first zero = wrong denominator! This gives fractions like 8/1000 instead of 8/10000. Always count every single decimal place from the decimal point to the last digit.

Practice Quiz

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How much of the whole does the shaded area (blue) represent?

FAQ

Everything you need to know about this question

How do I know what denominator to use?

Count the decimal places in your number. Each place represents a power of 10: 1 place = 10, 2 places = 100, 3 places = 1000, 4 places = 10000, and so on.

Why isn't 8/1000 the right answer for 0.0008?

8/1000 = 0.008, which is different from 0.0008! The extra zero in 0.0008 means it's in the ten-thousandths place, not thousandths.

Do I need to simplify the fraction?

Not always! Check if the numerator and denominator share any common factors. For $\frac{8}{10000}$ , you could simplify by dividing both by 8 to get $\frac{1}{1250}$ .

What if the decimal has zeros in the middle?

Count all decimal places, including zeros! For example, 0.0508 has 4 decimal places, so it becomes $\frac{508}{10000}$ .

How can I check if my fraction is correct?

Divide the numerator by the denominator using long division or a calculator. The result should equal your original decimal exactly!

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