Express 7.13 in Different Mathematical Forms: Decimal Conversion

Q: How do I know what denominator to use for the decimal part?

Count the decimal places! One decimal place = 10, two decimal places = 100, three = 1000. Since 0.13 has two decimal places, use 100.

Q: Why is 7.13 not equal to 7 11/100?

Because $ 7\frac{11}{100} = 7.11 $, not 7.13! The numerator must match the decimal digits exactly: 13 in the decimal becomes 13 in the numerator.

Q: What if I have a longer decimal like 7.135?

Count three decimal places, so use 1000: $ 7.135 = 7\frac{135}{1000} $. Then simplify if possible by finding common factors.

Q: How can I check my answer is correct?

Convert your mixed number back to decimal: $ 7\frac{13}{100} = 7 + \frac{13}{100} = 7 + 0.13 = 7.13 $ ✓

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to mixed fraction

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

00:07 Convert the remainder to a fraction

00:18 Combine into a mixed fraction

00:22 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$7.13=$

2

Step-by-step solution

To convert the decimal 7.13 into a mixed number with 100 as the denominator, we follow these steps:

Step 1: Identify the integer part of the decimal, which is 7.
Step 2: Convert the decimal part 0.13 into a fraction.
- The number 13 is in the hundredths place, which translates to the fraction $\frac{13}{100}$ .
Step 3: Combine the integer part with the fractional part to form the mixed number:
- Therefore, $7.13 = 7 \frac{13}{100}$ .

As a result, the decimal 7.13 is equivalent to the mixed number $7\frac{13}{100}$ .

3

Final Answer

$7\frac{13}{100}$

Key Points to Remember

Essential concepts to master this topic

Rule: Decimal places determine denominator power of 10
Technique: 0.13 has 2 decimal places = $\frac{13}{100}$
Check: Convert back: $7\frac{13}{100} = 7 + 0.13 = 7.13$ ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator for decimal places
Don't put 0.13 as $\frac{13}{10}$ = 1.3, not 0.13! This happens when you count decimal places wrong. Always count carefully: 0.13 has 2 decimal places, so use 100 as denominator.

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 for the decimal part?

+

Count the decimal places! One decimal place = 10, two decimal places = 100, three = 1000. Since 0.13 has two decimal places, use 100.

Why is 7.13 not equal to 7 11/100?

+

Because $7\frac{11}{100} = 7.11$ , not 7.13! The numerator must match the decimal digits exactly: 13 in the decimal becomes 13 in the numerator.

Can I simplify the fraction 13/100?

+

Check if 13 and 100 share common factors. Since 13 is prime and doesn't divide 100, $\frac{13}{100}$ is already in lowest terms.

What if I have a longer decimal like 7.135?

+

Count three decimal places, so use 1000: $7.135 = 7\frac{135}{1000}$ . Then simplify if possible by finding common factors.

How can I check my answer is correct?

+

Convert your mixed number back to decimal: $7\frac{13}{100} = 7 + \frac{13}{100} = 7 + 0.13 = 7.13$ ✓

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Express 7.13 in Different Mathematical Forms: Decimal Conversion

Decimal Conversion with Mixed Numbers

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