Convert Fraction to Decimal: Solving 74/1000 Step-by-Step

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

When dividing by powers of 10, you're making the number smaller. Moving left makes numbers smaller, just like $ 5.0 \rightarrow 0.5 $ when dividing by 10.

Q: How many places do I move for different denominators?

Count the zeros! 10 = 1 place, 100 = 2 places, 1000 = 3 places. The number of zeros equals the number of decimal places to move.

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

Add zeros! For $ \frac{5}{1000} $, you need 3 places: 5 → 0.5 → 0.05 → 0.005. Fill empty spots with zeros.

Q: Do I need to keep trailing zeros?

Usually no! $ 0.0740 = 0.074 $ because trailing zeros after the decimal don't change the value. Keep them only if specifically asked.

Q: How can I check my answer?

Multiply your decimal by the original denominator: $ 0.074 \times 1000 = 74 $. If you get the numerator back, you're correct!

Fraction to Decimal with Powers of Ten

Convert $\frac{74}{1000}$ into decimal form:

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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.

00:09 Remember, if the denominator is one thousand, then the numerator becomes the decimal number.

00:17 When dividing by one thousand, move the decimal point three places to the left.

00:25 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert $\frac{74}{1000}$ into decimal form:

Step-by-step solution

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

$74.0$

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

$.0740$

We'll add a zero before the decimal point as follows:

$0.0740=0.074$

Final Answer

0.074

Key Points to Remember

Essential concepts to master this topic

Rule: Dividing by powers of 10 moves decimal left
Technique: 1000 has 3 zeros, so move decimal 3 places left
Check: Multiply back: 0.074 × 1000 = 74 ✓

Common Mistakes

Avoid these frequent errors

Moving decimal point the wrong direction
Don't move the decimal right when dividing by 1000 = 740.0! This multiplies instead of divides. Always move decimal LEFT when dividing by powers of 10.

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?

When dividing by powers of 10, you're making the number smaller. Moving left makes numbers smaller, just like $5.0 \rightarrow 0.5$ when dividing by 10.

How many places do I move for different denominators?

Count the zeros! 10 = 1 place, 100 = 2 places, 1000 = 3 places. The number of zeros equals the number of decimal places to move.

What if I don't have enough digits?

Add zeros! For $\frac{5}{1000}$ , you need 3 places: 5 → 0.5 → 0.05 → 0.005. Fill empty spots with zeros.

Do I need to keep trailing zeros?

Usually no! $0.0740 = 0.074$ because trailing zeros after the decimal don't change the value. Keep them only if specifically asked.

How can I check my answer?

Multiply your decimal by the original denominator: $0.074 \times 1000 = 74$ . If you get the numerator back, you're correct!

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