Solve the Decimal Division: 0.5 ÷ 500 Step by Step

Q: Why is the answer so much smaller than 0.5?

When you divide by a large number like 500, you're splitting 0.5 into 500 tiny pieces. Each piece becomes very small - that's why $ 0.5 \div 500 = 0.001 $!

Q: How do I know how many decimal places the answer will have?

Look at the dividend and divisor. Here, 0.5 has 1 decimal place, and dividing by 500 creates more decimal places. The exact number depends on the complete calculation.

Q: Can I use fractions instead of decimals?

Absolutely! Convert $ 0.5 = \frac{1}{2} $, then $ \frac{1}{2} \div 500 = \frac{1}{2} \times \frac{1}{500} = \frac{1}{1000} = 0.001 $. Same answer!

Q: How can I check if 0.001 is really correct?

Use inverse operations! Since division and multiplication are opposites, check: $ 0.001 \times 500 = 0.5 $ ✓ If this equals your original number, you're right!

Q: What if I get confused by all the zeros?

Count carefully and use place value names: 0.001 is "one thousandth." You can also write it as $ \frac{1}{1000} $ to make the size clearer.

Decimal Division with Very Small Quotients

$0.5:500=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solution

00:05 Multiply each factor by 10 to eliminate the decimal point

00:33 Convert division to fraction

00:36 Break down each factor into multiplication with factor 5

00:44 Reduce what's possible

00:50 According to the number of zeros in the denominator, we'll move the decimal point

01:06 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

$0.5:500=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Convert $0.5$ to a fraction if necessary.
Step 2: Divide $0.5$ by $500$ using decimal division or treat $0.5$ as $\frac{1}{2}$ .
Step 3: Simplify the result to a standard decimal number.

Now, let's work through each step:
Step 1: The number $0.5$ can be considered as $\frac{1}{2}$ . However, dividing directly $0.5 \div 500$ is suited here.
Step 2: Express this division as a multiplication: $0.5 \times \frac{1}{500}$ .
Simplifying, we have: $0.5 \times 0.002 = 0.001$ Hence, the computation as division directly: $\frac{0.5}{500} = 0.001$

Step 3: Utilize division to achieve a simpler form, yielding the decimal $0.001$ .

Thus, the solution to the problem is clearly established as $0.001$ .

Final Answer

$0.001$

Key Points to Remember

Essential concepts to master this topic

Rule: When dividing a decimal by a large whole number, expect a very small result
Technique: Convert to multiplication: $0.5 \div 500 = 0.5 \times \frac{1}{500} = 0.001$
Check: Verify by multiplication: $0.001 \times 500 = 0.5$ ✓

Common Mistakes

Avoid these frequent errors

Moving decimal point incorrectly when dividing by large numbers
Don't just count zeros in 500 and move the decimal point 3 places left from 0.5 to get 0.0005! This ignores the actual division process. Always perform the complete division: 0.5 ÷ 500 = 0.001, or convert to multiplication with the reciprocal.

Practice Quiz

Test your knowledge with interactive questions

$\text{0}.07\times10=$

FAQ

Everything you need to know about this question

Why is the answer so much smaller than 0.5?

When you divide by a large number like 500, you're splitting 0.5 into 500 tiny pieces. Each piece becomes very small - that's why $0.5 \div 500 = 0.001$ !

How do I know how many decimal places the answer will have?

Look at the dividend and divisor. Here, 0.5 has 1 decimal place, and dividing by 500 creates more decimal places. The exact number depends on the complete calculation.

Can I use fractions instead of decimals?

Absolutely! Convert $0.5 = \frac{1}{2}$ , then $\frac{1}{2} \div 500 = \frac{1}{2} \times \frac{1}{500} = \frac{1}{1000} = 0.001$ . Same answer!

How can I check if 0.001 is really correct?

Use inverse operations! Since division and multiplication are opposites, check: $0.001 \times 500 = 0.5$ ✓ If this equals your original number, you're right!

What if I get confused by all the zeros?

Count carefully and use place value names: 0.001 is "one thousandth." You can also write it as $\frac{1}{1000}$ to make the size clearer.

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