Convert the Fraction: Solving 30/1000 to Decimal Form

Q: Why do I move the decimal point left instead of right?

When dividing by powers of ten, you move left because you're making the number smaller! Think: 30 ÷ 10 = 3.0, 30 ÷ 100 = 0.30, 30 ÷ 1000 = 0.030.

Q: How do I remember how many places to move?

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

Q: What if my numerator has fewer digits than places to move?

Add placeholder zeros to the left! For $ \frac{5}{1000} $, think of 5 as 005, then move 3 places left to get 0.005.

Q: Do I need to keep the trailing zero in 0.030?

No! In decimal form, 0.030 = 0.03. The trailing zero doesn't change the value, so 0.03 is the simplest form.

Q: Can I just do regular division instead?

Yes, but moving the decimal point is much faster! Both methods give the same answer: 30 ÷ 1000 = 0.03.

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

00:06 Based on the denominator, we'll know how many places to move the decimal point to the left

00:12 The denominator has 3 zeros, so we'll move the decimal point 3 places to the left

00:21 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

$\frac{30}{1000}=$

2

Step-by-step solution

To convert the fraction $\frac{30}{1000}$ to a decimal:

Step 1: Recognize the fraction $\frac{30}{1000}$ has a direct conversion due to the denominator being a power of ten, which makes it straightforward to convert directly to a decimal.
Step 2: Divide the numerator by the denominator: $\frac{30}{1000} = 30 \div 1000$ .
Step 3: Perform the division: When dividing 30 by 1000, shift the decimal point in the numerator three places to the left (since 1000 is $10^3$ ): $30 \div 1000 = 0.03$ .

Therefore, the solution to the problem is $0.03$ .

3

Final Answer

$0.03$

Key Points to Remember

Essential concepts to master this topic

Rule: Powers of ten denominators convert directly to decimals
Technique: Move decimal point left: $\frac{30}{1000}$ = 3 places left = 0.030
Check: Verify 0.03 × 1000 = 30 matches original numerator ✓

Common Mistakes

Avoid these frequent errors

Counting decimal places incorrectly
Don't move the decimal point only 2 places for 1000 = 0.30 instead of 0.03! This happens when you count zeros instead of total digits. Always count that 1000 = 10³, so move 3 places left.

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 instead of right?

+

When dividing by powers of ten, you move left because you're making the number smaller! Think: 30 ÷ 10 = 3.0, 30 ÷ 100 = 0.30, 30 ÷ 1000 = 0.030.

How do I remember how many places to move?

+

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

What if my numerator has fewer digits than places to move?

+

Add placeholder zeros to the left! For $\frac{5}{1000}$ , think of 5 as 005, then move 3 places left to get 0.005.

Do I need to keep the trailing zero in 0.030?

+

No! In decimal form, 0.030 = 0.03. The trailing zero doesn't change the value, so 0.03 is the simplest form.

Can I just do regular division instead?

+

Yes, but moving the decimal point is much faster! Both methods give the same answer: 30 ÷ 1000 = 0.03.

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Convert the Fraction: Solving 30/1000 to Decimal Form

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