Convert Fraction to Decimal: Changing 5/1000 to Its Decimal Form

Q: How do I know where to put the 5 in the decimal?

Count the zeros in the denominator! Since 1000 has 3 zeros, you need exactly 3 decimal places. Put 5 in the third position: 0.005.

Q: Why isn't the answer 0.5 or 0.05?

Those answers don't match the denominator! $ \frac{5}{10} = 0.5 $ and $ \frac{5}{100} = 0.05 $, but we have $ \frac{5}{1000} $ which needs three decimal places.

Q: What's the pattern for converting fractions with 10, 100, 1000?

It's all about counting zeros:$ \frac{n}{10} $ → 1 decimal place$ \frac{n}{100} $ → 2 decimal places$ \frac{n}{1000} $ → 3 decimal places

Q: How can I double-check my answer?

Convert your decimal back to a fraction! If 0.005 = $ \frac{5}{1000} $, then you got it right. You can also think: 5 thousandths should be a very small number.

Q: What if I need to add zeros before the 5?

Always add placeholder zeros! For $ \frac{5}{1000} $, you write 0.005, not just .5. The zeros show that 5 is specifically in the thousandths place.

Fraction Conversion with Thousandths Place Value

Convert $\frac{5}{1000}$ into a decimal.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's convert this to a decimal fraction.

00:07 The number of zeros in the denominator tells us how many places to move the decimal point left.

00:14 There are three zeros, so we'll move the decimal point three places to the left.

00:19 Put the numerator so that there are three digits after the decimal point.

00:25 Fill in any missing digits with zeros.

00:29 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert $\frac{5}{1000}$ into a decimal.

Step-by-step solution

To convert the fraction $\frac{5}{1000}$ into a decimal, consider the following steps:

Step 1: Recognize that the denominator 1000 represents thousandths. We need to express 5 in terms of thousandths.
Step 2: Convert the fraction to a decimal by aligning with the place value: $\frac{5}{1000}$ is equivalent to 5 thousandths.
Step 3: The decimal form therefore has the digit 5 in the thousandths place, which results in the number 0.005.

Since the denominator is 1000, equivalent to three decimal places, the number 5 as part of thousandths results in $0.005$ .

Therefore, the solution to the problem is $\frac{5}{1000} = 0.005$ . This corresponds to choice 2.

Final Answer

0.005

Key Points to Remember

Essential concepts to master this topic

Place Value: Denominator 1000 means the thousandths decimal place
Technique: Put digit 5 in thousandths place: 0.005
Check: Count decimal places - three zeros means three places ✓

Common Mistakes

Avoid these frequent errors

Placing digit in wrong decimal position
Don't put 5 in tenths place getting 0.5 or hundredths getting 0.05 = wrong place value! The denominator 1000 has three zeros, which means exactly three decimal places. Always count the zeros in the denominator to find correct decimal position.

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 where to put the 5 in the decimal?

Count the zeros in the denominator! Since 1000 has 3 zeros, you need exactly 3 decimal places. Put 5 in the third position: 0.005.

Why isn't the answer 0.5 or 0.05?

Those answers don't match the denominator! $\frac{5}{10} = 0.5$ and $\frac{5}{100} = 0.05$ , but we have $\frac{5}{1000}$ which needs three decimal places.

What's the pattern for converting fractions with 10, 100, 1000?

It's all about counting zeros:

$\frac{n}{10}$ → 1 decimal place
$\frac{n}{100}$ → 2 decimal places
$\frac{n}{1000}$ → 3 decimal places

How can I double-check my answer?

Convert your decimal back to a fraction! If 0.005 = $\frac{5}{1000}$ , then you got it right. You can also think: 5 thousandths should be a very small number.

What if I need to add zeros before the 5?

Always add placeholder zeros! For $\frac{5}{1000}$ , you write 0.005, not just .5. The zeros show that 5 is specifically in the thousandths place.

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