Simplify the Fraction: Converting 12/200 to Its Simplest Form

Q: Why should I simplify the fraction before converting to decimal?

Simplifying first makes the division much easier! Converting $ \frac{3}{50} $ is simpler than $ \frac{12}{200} $, and you're less likely to make calculation errors.

Q: How do I find the GCD of 12 and 200?

List the factors: 12 = 2² × 3, and 200 = 2³ × 5². The common factors are 2², so GCD = 4. Divide both numerator and denominator by 4.

Q: Can I just use a calculator to convert the fraction?

Yes, but simplifying first helps you understand the relationship between fractions and decimals. Plus, $ \frac{3}{50} $ is easier to work with in future problems!

Q: What if my decimal has more than two places?

That's normal! Some fractions create repeating decimals or longer decimal expansions. Round to the required number of decimal places if asked.

Fraction to Decimal Conversion with Simplification

$\frac{12}{200}=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to decimal fraction

00:03 Convert the fraction so the denominator is a multiple of 10

00:06 Make sure to divide both numerator and denominator

00:15 Write the numerator as a number

00:18 Now according to the denominator move the decimal point left

00:21 There are 2 zeros in the denominator, so move 2 times left

00:27 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

$\frac{12}{200}=\text{ ?}$

Step-by-step solution

Let's divide both the numerator and denominator by 2 to get 100 in the denominator:

$\frac{12:2}{200:2}=\frac{6}{100}$

Now let's rewrite the simple fraction as a decimal fraction:

$6.0$

Since the fraction is divisible by 100, we move the decimal point two places to the left:

$.060$

Now let's add the zero before the decimal point to get:

$0.060=0.06$

Final Answer

0.06

Key Points to Remember

Essential concepts to master this topic

Simplify First: Find GCD of numerator and denominator before converting
Technique: Divide both 12 and 200 by 4 to get $\frac{3}{50}$
Check: Verify $\frac{3}{50} = 0.06$ by multiplying 0.06 × 50 = 3 ✓

Common Mistakes

Avoid these frequent errors

Converting fraction to decimal without simplifying first
Don't convert $\frac{12}{200}$ directly to decimal = harder division and more chance for errors! Working with large numbers increases calculation mistakes. Always simplify the fraction first by finding the GCD, then convert the simpler fraction to decimal.

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 should I simplify the fraction before converting to decimal?

Simplifying first makes the division much easier! Converting $\frac{3}{50}$ is simpler than $\frac{12}{200}$ , and you're less likely to make calculation errors.

How do I find the GCD of 12 and 200?

List the factors: 12 = 2² × 3, and 200 = 2³ × 5². The common factors are 2², so GCD = 4. Divide both numerator and denominator by 4.

Can I just use a calculator to convert the fraction?

Yes, but simplifying first helps you understand the relationship between fractions and decimals. Plus, $\frac{3}{50}$ is easier to work with in future problems!

What if my decimal has more than two places?

That's normal! Some fractions create repeating decimals or longer decimal expansions. Round to the required number of decimal places if asked.

How can I check if 0.06 is correct?

Multiply your decimal by the original denominator: 0.06 × 200 = 12 ✓. If you get the original numerator, your answer is correct!

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