Express the Decimal: Finding All Equivalent Forms of 1.1

Q: Why is 1.1 equal to 11/10 and not 1 1/10?

Both are correct! $ \frac{11}{10} $ is an improper fraction, while $ 1\frac{1}{10} $ is a mixed number. They represent the same value, just written differently.

Q: How do I know what denominator to use?

Count the decimal places! One decimal place means tenths (denominator 10), two places means hundredths (denominator 100), and so on.

Q: What if I get 1.10 instead of 1.1?

They're the same value! 1.10 = 1.1 because trailing zeros after the decimal don't change the number's value. Both equal $ \frac{11}{10} $.

Q: Can I simplify 11/10 further?

No, $ \frac{11}{10} $ is already in simplest form because 11 and 10 share no common factors other than 1.

Q: Why do we add 10/10 + 1/10 instead of just writing 11/10?

Breaking it down helps you understand where each part comes from! The whole number 1 becomes $ \frac{10}{10} $, and 0.1 becomes $ \frac{1}{10} $. This method works for any decimal.

Decimal to Fraction with Place Value

$1.1=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to fraction

00:03 Break down the number into whole number and remainder

00:08 Convert the remainder to fraction

00:14 Convert from whole number to whole fraction

00:20 Add with common denominator

00:23 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

$1.1=$

Step-by-step solution

To convert the decimal $1.1$ into a fraction, we will follow these steps:

Step 1: Express $1.1$ as a sum: $1 + 0.1$ .
Step 2: Convert each part to a fraction.
Step 3: Simplify and add the fractions.

Now, let's work through each step:

Step 1: Express $1.1$ as:

$1.1 = 1 + 0.1$

Step 2: Convert each part to a fraction:
$1$ can be written as $\frac{10}{10}$ , and $0.1 = \frac{1}{10}$ .

Step 3: Add the fractions:

$\frac{10}{10} + \frac{1}{10} = \frac{10 + 1}{10} = \frac{11}{10}$

Therefore, the decimal $1.1$ as a fraction is $\frac{11}{10}$ .

Final Answer

$\frac{11}{10}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Each decimal place represents a power of 10
Technique: 1.1 = 1 + 0.1 = 10/10 + 1/10
Check: Convert back: 11/10 = 11 ÷ 10 = 1.1 ✓

Common Mistakes

Avoid these frequent errors

Misinterpreting decimal place values
Don't write 1.1 as 11/100 because you count two digits = wrong denominator! The decimal 1.1 has one digit after the decimal point, so use 10 as denominator. Always count decimal places to determine the correct power 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 is 1.1 equal to 11/10 and not 1 1/10?

Both are correct! $\frac{11}{10}$ is an improper fraction, while $1\frac{1}{10}$ is a mixed number. They represent the same value, just written differently.

How do I know what denominator to use?

Count the decimal places! One decimal place means tenths (denominator 10), two places means hundredths (denominator 100), and so on.

What if I get 1.10 instead of 1.1?

They're the same value! 1.10 = 1.1 because trailing zeros after the decimal don't change the number's value. Both equal $\frac{11}{10}$ .

Can I simplify 11/10 further?

No, $\frac{11}{10}$ is already in simplest form because 11 and 10 share no common factors other than 1.

Why do we add 10/10 + 1/10 instead of just writing 11/10?

Breaking it down helps you understand where each part comes from! The whole number 1 becomes $\frac{10}{10}$ , and 0.1 becomes $\frac{1}{10}$ . This method works for any decimal.

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