Convert Mixed Number 9 1/1000 to Decimal Form: Step-by-Step

Q: How do I know which decimal place to use?

Count the zeros in the denominator! The denominator 1000 has 3 zeros, so $ \frac{1}{1000} $ goes to the third decimal place (thousandths): 0.001.

Q: Why isn't the answer 9.1 or 9.10?

Those put the 1 in the wrong decimal place! 9.1 means $ 9\frac{1}{10} $ and 9.10 means $ 9\frac{10}{100} $. We need $ 9\frac{1}{1000} = 9.001 $.

Q: Do I always add the whole number and decimal parts?

Yes! Mixed numbers are always the sum of the whole number and the fraction. So $ 9\frac{1}{1000} = 9 + \frac{1}{1000} = 9 + 0.001 = 9.001 $.

Q: How can I remember decimal place values?

Use this pattern: tenths, hundredths, thousandths. The denominator tells you: 10 → first place, 100 → second place, 1000 → third place after the decimal point.

Q: What if the fraction has a different numerator?

The process stays the same! For example, $ \frac{7}{1000} = 0.007 $. The denominator still determines the decimal place, and the numerator becomes the digit in that place.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's convert this to a decimal fraction.

00:07 First, break the number into a whole number and a remainder.

00:21 If the denominator is 1,000, place the numerator three places after the decimal point.

00:32 Now, add this to the decimal fraction.

00:42 Use long addition to calculate the sum.

00:51 Calculate carefully and substitute the values as needed.

01:07 And there you have it! That's the solution to our question.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Convert $9\frac{1}{1000}$ into a decimal.

2

Step-by-step solution

To solve this problem, we need to convert the mixed number $9\frac{1}{1000}$ into its decimal form. Let's execute this in a series of well-defined steps:

Step 1: Convert the fractional part to a decimal.
The fraction $\frac{1}{1000}$ corresponds to the thousandths place. Thus, $\frac{1}{1000} = 0.001$ .
Step 2: Combine the whole number and the decimal.
The whole number part of our mixed number is 9. To convert $9\frac{1}{1000}$ to a decimal, we simply add the decimal fraction to the whole number. Therefore, we have: $9 + 0.001 = 9.001$

Therefore, the decimal representation of $9\frac{1}{1000}$ is 9.001.

The correct choice from the given options is $\boxed{9.001}$ .

3

Final Answer

9.001

Key Points to Remember

Essential concepts to master this topic

Rule: Mixed numbers equal whole number plus fractional part
Technique: Convert $\frac{1}{1000} = 0.001$ using place value
Check: Verify $9 + 0.001 = 9.001$ matches original mixed number ✓

Common Mistakes

Avoid these frequent errors

Confusing decimal place values with denominators
Don't write $\frac{1}{1000}$ as 9.10 or 9.1 = wrong place value! Students often put the 1 in tenths or hundredths instead of thousandths. Always count decimal places: 1000 has 3 zeros, so the 1 goes in the third decimal place (thousandths).

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

How do I know which decimal place to use?

+

Count the zeros in the denominator! The denominator 1000 has 3 zeros, so $\frac{1}{1000}$ goes to the third decimal place (thousandths): 0.001.

Why isn't the answer 9.1 or 9.10?

+

Those put the 1 in the wrong decimal place! 9.1 means $9\frac{1}{10}$ and 9.10 means $9\frac{10}{100}$ . We need $9\frac{1}{1000} = 9.001$ .

Do I always add the whole number and decimal parts?

+

Yes! Mixed numbers are always the sum of the whole number and the fraction. So $9\frac{1}{1000} = 9 + \frac{1}{1000} = 9 + 0.001 = 9.001$ .

How can I remember decimal place values?

+

Use this pattern: tenths, hundredths, thousandths. The denominator tells you: 10 → first place, 100 → second place, 1000 → third place after the decimal point.

What if the fraction has a different numerator?

+

The process stays the same! For example, $\frac{7}{1000} = 0.007$ . The denominator still determines the decimal place, and the numerator becomes the digit in that place.

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Convert Mixed Number 9 1/1000 to Decimal Form: Step-by-Step

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