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

00:00 Convert to decimal fraction

00:03 Break down the number into whole number and remainder

00:17 When the denominator equals 1000, place the numerator 3 digits after

00:28 Add to decimal fraction

00:38 Use long addition for calculation

00:47 Calculate and substitute accordingly

01:03 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 $9\frac{1}{1000}$ 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

Write the following fraction as a decimal:

$\frac{5}{100}=$

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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