Convert Decimal Number: Express 2.13 in Multiple Forms

Q: How do I know what denominator to use?

Count the decimal places! One decimal place = tenths (denominator 10), two decimal places = hundredths (denominator 100). Since 2.13 has two decimal places, use 100.

Q: What if I get confused between 0.13 and 13?

Remember: 0.13 is the decimal part and 13 is the numerator. The decimal 0.13 means "13 hundredths" which equals $ \frac{13}{100} $.

Q: Can I write this as an improper fraction instead?

Yes! $ 2\frac{13}{100} = \frac{200 + 13}{100} = \frac{213}{100} $. Both forms are correct, but mixed numbers are often preferred for decimals.

Q: How can I check my answer quickly?

Convert back to decimal: $ 2\frac{13}{100} = 2 + 0.13 = 2.13 $. If you get the original decimal, you're right!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to mixed number

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

00:08 Convert the remainder to a fraction

00:14 Add to mixed number

00:19 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$2.13=$

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the whole number part of $2.13$
Step 2: Convert the decimal part $0.13$ to a fraction
Step 3: Combine the whole number with the fraction

Let's work through each step:

Step 1: The whole number part of $2.13$ is $2$ .

Step 2: The decimal part is $0.13$ . Since there are two decimal places, it can be expressed as a fraction over 100. Specifically, $0.13 = \frac{13}{100}$ .

Step 3: Combine the whole number and fraction to form the mixed number. Thus, $2.13$ can be expressed as $2 \frac{13}{100}$ .

Therefore, the solution to the problem is $2 \frac{13}{100}$ .

3

Final Answer

$2\frac{13}{100}$

Key Points to Remember

Essential concepts to master this topic

Place Value: Two decimal places means denominator is 100
Technique: Keep whole number 2, convert 0.13 to 13/100
Check: Convert back: 2 + 13/100 = 2.13 ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator based on decimal digits
Don't use 13 as the denominator because there are 13 hundredths = $\frac{13}{13}$ ! This ignores place value rules. Always use 100 as denominator when there are exactly two decimal places.

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

How do I know what denominator to use?

+

Count the decimal places! One decimal place = tenths (denominator 10), two decimal places = hundredths (denominator 100). Since 2.13 has two decimal places, use 100.

Do I need to simplify the fraction 13/100?

+

Check if 13 and 100 share any common factors. Since 13 is prime and doesn't divide 100, 13/100 is already in simplest form!

What if I get confused between 0.13 and 13?

+

Remember: 0.13 is the decimal part and 13 is the numerator. The decimal 0.13 means "13 hundredths" which equals $\frac{13}{100}$ .

Can I write this as an improper fraction instead?

+

Yes! $2\frac{13}{100} = \frac{200 + 13}{100} = \frac{213}{100}$ . Both forms are correct, but mixed numbers are often preferred for decimals.

How can I check my answer quickly?

+

Convert back to decimal: $2\frac{13}{100} = 2 + 0.13 = 2.13$ . If you get the original decimal, you're right!

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Convert Decimal Number: Express 2.13 in Multiple Forms

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