Convert the Fraction: Finding the Decimal Value of 11/1000

Q: How do I remember which way to move the decimal point?

Think logically: dividing makes numbers smaller, so the decimal point moves left. Dividing by 1000 means the result is much smaller than the original number!

Q: What if there aren't enough digits to move the decimal?

Add zeros as placeholders! For $ \frac{11}{1000} $, start with 11.0, then add zeros: 11.0 → 0.011. The zeros help you place the decimal correctly.

Q: Why does 1000 in the denominator mean 3 decimal places?

Count the zeros in 1000: there are 3 zeros, so move the decimal point 3 places left. This pattern works for all powers of 10: 10 = 1 place, 100 = 2 places, 1000 = 3 places.

Q: How can I check if 0.011 is really equal to 11/1000?

Multiply your decimal answer by the original denominator: 0.011 × 1000 = 11. If you get the original numerator back, your conversion is correct!

Q: What's the difference between 0.011 and 0.11?

$ 0.011 = \frac{11}{1000} $ while $ 0.11 = \frac{11}{100} $. The extra zero makes a big difference! 0.011 is much smaller than 0.11.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to decimal fraction

00:03 Write the numerator as a number

00:09 Now according to the denominator, move the decimal point to the left

00:12 There are 3 zeros in the denominator, so we move 3 times to the left

00:19 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

$\frac{11}{1000}=$

2

Step-by-step solution

Let's write the simple fraction as a decimal fraction:

$11.0$

Since the fraction is divided by 1000, we move the decimal point three times to the left:

$.0110$

Now let's add the zero before the decimal point and we get:

$0.0110=0.011$

3

Final Answer

0.011

Key Points to Remember

Essential concepts to master this topic

Rule: When denominator is 1000, move decimal point 3 places left
Technique: Convert 11 to 11.0, then shift: 11.0 → 0.011
Check: Multiply back: 0.011 × 1000 = 11 ✓

Common Mistakes

Avoid these frequent errors

Moving decimal point the wrong direction or wrong number of places
Don't move the decimal point right or only 1-2 places = wrong decimal value! Moving right makes the number bigger, not smaller, and wrong place count gives incorrect decimals. Always count zeros in denominator and move decimal point left that many places.

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 remember which way to move the decimal point?

+

Think logically: dividing makes numbers smaller, so the decimal point moves left. Dividing by 1000 means the result is much smaller than the original number!

What if there aren't enough digits to move the decimal?

+

Add zeros as placeholders! For $\frac{11}{1000}$ , start with 11.0, then add zeros: 11.0 → 0.011. The zeros help you place the decimal correctly.

Why does 1000 in the denominator mean 3 decimal places?

+

Count the zeros in 1000: there are 3 zeros, so move the decimal point 3 places left. This pattern works for all powers of 10: 10 = 1 place, 100 = 2 places, 1000 = 3 places.

How can I check if 0.011 is really equal to 11/1000?

+

Multiply your decimal answer by the original denominator: 0.011 × 1000 = 11. If you get the original numerator back, your conversion is correct!

What's the difference between 0.011 and 0.11?

+

$0.011 = \frac{11}{1000}$ while $0.11 = \frac{11}{100}$ . The extra zero makes a big difference! 0.011 is much smaller than 0.11.

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Convert the Fraction: Finding the Decimal Value of 11/1000

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