Convert Fraction to Decimal: Solving 100/1000 Step-by-Step

Q: Why are 0.1, 0.10, and 0.100 all correct answers?

These are equivalent decimal representations of the same value! Adding zeros after the decimal doesn't change the number's value - it just shows different levels of precision.

Q: Do I always need to simplify fractions before converting?

It's highly recommended! Simplifying $ \frac{100}{1000} $ to $ \frac{1}{10} $ makes the conversion much easier and reduces calculation errors.

Q: How do I know when a fraction is fully simplified?

A fraction is simplified when the greatest common factor (GCF) of the numerator and denominator is 1. For $ \frac{100}{1000} $, the GCF is 100.

Q: What if I can't see the common factor immediately?

Try dividing both numbers by 10, 100, or 1000 first. For fractions with many zeros, this often reveals the simplification quickly!

Q: Are there other ways to convert this fraction to decimal?

Yes! You can also use long division: divide 100 by 1000 directly. But simplifying first makes the work much easier.

Q: When would I use 0.100 instead of 0.1?

Use 0.100 when you need to show precision to the thousandths place, like in scientific measurements or when matching the format of other numbers in your work.

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 We'll look at the number of zeros in the denominator. This tells us how far to move the decimal point to the left.

00:13 Here, we have three zeros, so we move the decimal point three places to the left.

00:19 Position the numerator three digits after the decimal point.

00:28 Next, we remove any extra zeros.

00:35 And that's how we find the answer!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Convert $\frac{100}{1000}$ into a decimal.

2

Step-by-step solution

To solve this problem, let us follow these steps:

Step 1: Understand the given fraction $\frac{100}{1000}$ .
Step 2: Simplify the fraction if possible.
Step 3: Convert the simplified fraction into a decimal.

Now, let's dive into the details:

Step 1: We are given $\frac{100}{1000}$ . This fraction represents 100 divided by 1000.

Step 2: The fraction can be simplified because both the numerator (100) and denominator (1000) have a common factor of 100.
Dividing both by 100 gives:

\frac{100}{1000} = \frac{1}{10}

Step 3: Convert $\frac{1}{10}$ into a decimal:

The fraction $\frac{1}{10}$ means one-tenth, which can be directly written as the decimal $0.1$ .

There are also other decimal forms which retain the same value such as $0.10$ and $0.100$ , which are legitimate representations with different coverage of decimal precision.

Therefore, the decimal representation of $\frac{100}{1000}$ is 0.1, and among the choices provided, the answer choice representing this is "All answers are correct".

3

Final Answer

All answers are correct

Key Points to Remember

Essential concepts to master this topic

Simplification: Divide numerator and denominator by their greatest common factor
Technique: $\frac{100}{1000} = \frac{1}{10}$ by dividing both by 100
Check: Verify 0.1 = 0.10 = 0.100 are all equivalent representations ✓

Common Mistakes

Avoid these frequent errors

Thinking decimal forms with different trailing zeros are different values
Don't think 0.1, 0.10, and 0.100 are different numbers = confusion about equivalent forms! These represent the exact same value with different decimal precision. Always remember trailing zeros after the decimal point don't change the value.

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

$$ 0.38= $$

FAQ

Everything you need to know about this question

Why are 0.1, 0.10, and 0.100 all correct answers?

+

These are equivalent decimal representations of the same value! Adding zeros after the decimal doesn't change the number's value - it just shows different levels of precision.

Do I always need to simplify fractions before converting?

+

It's highly recommended! Simplifying $\frac{100}{1000}$ to $\frac{1}{10}$ makes the conversion much easier and reduces calculation errors.

How do I know when a fraction is fully simplified?

+

A fraction is simplified when the greatest common factor (GCF) of the numerator and denominator is 1. For $\frac{100}{1000}$ , the GCF is 100.

What if I can't see the common factor immediately?

+

Try dividing both numbers by 10, 100, or 1000 first. For fractions with many zeros, this often reveals the simplification quickly!

Are there other ways to convert this fraction to decimal?

+

Yes! You can also use long division: divide 100 by 1000 directly. But simplifying first makes the work much easier.

When would I use 0.100 instead of 0.1?

+

Use 0.100 when you need to show precision to the thousandths place, like in scientific measurements or when matching the format of other numbers in your work.

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Convert Fraction to Decimal: Solving 100/1000 Step-by-Step

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