Convert Fraction to Decimal: Solving 6/1000 Step-by-Step

Q: Why do I move the decimal point left when dividing?

Division makes numbers smaller, so the decimal point moves left. Think of it this way: $ \frac{6}{1000} $ means "6 divided into 1000 equal parts," which gives a very small piece!

Q: How many places do I move the decimal point?

Count the zeros in the denominator! 1000 has 3 zeros, so move 3 places left. 100 has 2 zeros = move 2 places, and so on.

Q: What if I don't have enough digits to move left?

Add leading zeros! For $ \frac{6}{1000} $, start with 6.0, then add zeros as you move: 0.6 → 0.06 → 0.006.

Q: Do I need to keep trailing zeros in my answer?

No! Once you've moved the decimal point, you can drop trailing zeros. So 0.0060 becomes 0.006, but never drop zeros between the decimal and the first non-zero digit.

Q: How can I check if my decimal is correct?

Convert back to a fraction! 0.006 = $ \frac{6}{1000} $ because 0.006 means "6 thousandths." If it matches your original fraction, you're right!

Fraction to Decimal with Powers of Ten

Convert to decimal form:

$\frac{6}{1000}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to decimal fraction

00:04 First, let's write the numerator as a number

00:08 Now according to the denominator, we'll move the decimal point to the left

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

00:18 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert to decimal form:

$\frac{6}{1000}=$

Step-by-step solution

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

$6.0$

Given that the fraction divides by 1000, we move the decimal point three places to the left:

$.0060$

We fill in the zero before the decimal point as follows:

$0.0060=0.006$

Final Answer

0.006

Key Points to Remember

Essential concepts to master this topic

Rule: Dividing by 1000 moves decimal point three places left
Technique: Start with 6.0, then move: 6.0 → 0.60 → 0.060 → 0.006
Check: Count decimal places: 0.006 has 3 places, matching 1000's three zeros ✓

Common Mistakes

Avoid these frequent errors

Moving decimal point the wrong direction
Don't move the decimal point to the right when dividing by 1000 = gets 60.0 instead of 0.006! Division makes numbers smaller, not larger. Always move the decimal point LEFT when dividing by powers of ten.

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 do I move the decimal point left when dividing?

Division makes numbers smaller, so the decimal point moves left. Think of it this way: $\frac{6}{1000}$ means "6 divided into 1000 equal parts," which gives a very small piece!

How many places do I move the decimal point?

Count the zeros in the denominator! 1000 has 3 zeros, so move 3 places left. 100 has 2 zeros = move 2 places, and so on.

What if I don't have enough digits to move left?

Add leading zeros! For $\frac{6}{1000}$ , start with 6.0, then add zeros as you move: 0.6 → 0.06 → 0.006.

Do I need to keep trailing zeros in my answer?

No! Once you've moved the decimal point, you can drop trailing zeros. So 0.0060 becomes 0.006, but never drop zeros between the decimal and the first non-zero digit.

How can I check if my decimal is correct?

Convert back to a fraction! 0.006 = $\frac{6}{1000}$ because 0.006 means "6 thousandths." If it matches your original fraction, you're right!

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