Converting the Fraction 11/200 to Decimal Form: Step-by-Step Solution

Q: What if my denominator can't become a power of 10?

Some fractions like $ \frac{1}{3} $ create repeating decimals (0.333...). In these cases, long division is your best method, or express as a repeating decimal with a bar over the repeating digits.

Q: Is 0.055 the same as .055?

Yes! Both are correct, but 0.055 is preferred because the leading zero makes it clearer that this is a decimal less than 1. It prevents confusion and follows standard mathematical notation.

Q: How can I check if 0.055 is really equal to 11/200?

Convert back: 0.055 = $ \frac{55}{1000} $. Divide both by 5: $ \frac{55÷5}{1000÷5} = \frac{11}{200} $ ✓. Or use multiplication: 200 × 0.055 = 11 ✓

Fraction to Decimal with Denominator Conversion

Convert $\frac{11}{200}$ into a decimal.

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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 We want a denominator that's a multiple of 10 and 10

00:06 Therefore we'll expand the fraction, making sure to multiply both numerator and denominator

00:18 Convert to decimal fraction

00:21 When the denominator equals 1000

00:25 Place the numerator 3 digits after the decimal point

00:31 Place 0 in the missing digits

00:34 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

Convert $\frac{11}{200}$ into a decimal.

Step-by-step solution

To solve the problem of converting $\frac{11}{200}$ into a decimal, we will scale the fraction so the denominator becomes 1000, which facilitates easier conversion to a decimal number.

First, observe that:

The given fraction is $\frac{11}{200}$ .
We want the denominator to be a power of 10, such as 1000.
To do this, multiply both the numerator and the denominator by 5:

$\frac{11 \times 5}{200 \times 5} = \frac{55}{1000}$

Having the fraction $\frac{55}{1000}$ , it is straightforward to convert it to a decimal by placing the decimal point three places from the right in the numerator, because 1000 has three zeros.

This results in the decimal number:

$0.055$

Therefore, the decimal representation of $\frac{11}{200}$ is 0.055.

Final Answer

0.055

Key Points to Remember

Essential concepts to master this topic

Strategy: Convert denominator to power of 10 for easy decimal placement
Technique: Multiply $\frac{11}{200}$ by $\frac{5}{5}$ to get $\frac{55}{1000}$
Check: Count zeros in denominator: 1000 has 3 zeros, so 55 becomes 0.055 ✓

Common Mistakes

Avoid these frequent errors

Placing decimal point incorrectly after conversion
Don't count decimal places from the left or guess the position = wrong decimal like 5.5 or 0.55! The denominator 1000 has exactly 3 zeros, which determines decimal placement. Always count zeros in your power-of-10 denominator to place the decimal point correctly.

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 can't I just divide 11 by 200 directly?

You absolutely can! Division gives the same answer: 11 ÷ 200 = 0.055. The scaling method shown here helps you understand why decimals work and is useful when calculators aren't allowed.

How do I know what to multiply by to get a power of 10?

Look at your denominator's factors. Since 200 = 8 × 25 = 2³ × 5², you need more factors of 5 to make it 10³ = 1000. So multiply by $\frac{5}{5}$ to get 1000.

What if my denominator can't become a power of 10?

Some fractions like $\frac{1}{3}$ create repeating decimals (0.333...). In these cases, long division is your best method, or express as a repeating decimal with a bar over the repeating digits.

Is 0.055 the same as .055?

Yes! Both are correct, but 0.055 is preferred because the leading zero makes it clearer that this is a decimal less than 1. It prevents confusion and follows standard mathematical notation.

How can I check if 0.055 is really equal to 11/200?

Convert back: 0.055 = $\frac{55}{1000}$ . Divide both by 5: $\frac{55÷5}{1000÷5} = \frac{11}{200}$ ✓. Or use multiplication: 200 × 0.055 = 11 ✓

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