Complete the Decimal Expression: Finding the Value of 8.1 =

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

Look at the place value of the last digit! The first decimal place is tenths (denominator 10), the second is hundredths (denominator 100), and so on.

Q: Why isn't 8.1 equal to 8 and 1/50?

Because $ \frac{1}{50} = 0.02 $, not 0.1! Always check: what decimal does my fraction equal? Only $ \frac{1}{10} = 0.1 $.

Q: Do I need to simplify the fraction part?

Yes, always simplify! But $ \frac{1}{10} $ is already in lowest terms since 1 and 10 share no common factors other than 1.

Q: How can I double-check my mixed number is correct?

Convert it back to decimal! $ 8\frac{1}{10} = 8 + \frac{1}{10} = 8 + 0.1 = 8.1 $ ✓

Q: What if the decimal has more places, like 8.17?

Use the same method! $ 8.17 = 8 + 0.17 = 8 + \frac{17}{100} = 8\frac{17}{100} $. The denominator matches the place value of the last digit.

Decimal-Fraction Conversion with Tenths Place

$8.1=$

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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 fraction

00:11 Add to create mixed fraction

00:16 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

$8.1=$

Step-by-step solution

To solve this problem, we need to convert the decimal number $8.1$ into a mixed number.

Step 1: Recognize that the number $8.1$ can be broken into an integer part and a fractional part. The integer part is $8$ and the decimal part is $0.1$ .
Step 2: Convert the decimal part $0.1$ into a fraction. Since $0.1$ is equivalent to $\frac{1}{10}$ , we write $0.1 = \frac{1}{10}$ .
Step 3: Combine the integer part and the fractional part to form a mixed number. Thus, $8.1$ can be rewritten as $8 + \frac{1}{10}$ which simplifies to the mixed number $8 \frac{1}{10}$ .

Therefore, the solution to the problem is $8 \frac{1}{10}$ .

Final Answer

$8\frac{1}{10}$

Key Points to Remember

Essential concepts to master this topic

Place Value: The first decimal place represents tenths
Technique: Convert 0.1 to $\frac{1}{10}$ by reading place value
Check: Verify $8\frac{1}{10} = 8 + 0.1 = 8.1$ ✓

Common Mistakes

Avoid these frequent errors

Converting 0.1 to incorrect denominators
Don't convert 0.1 to $\frac{1}{100}$ or $\frac{1}{50}$ = wrong fraction! This happens when students confuse place values. Always remember the first decimal place is tenths, so 0.1 = $\frac{1}{10}$ .

Practice Quiz

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How much of the whole does the shaded area (blue) represent?

FAQ

Everything you need to know about this question

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

Look at the place value of the last digit! The first decimal place is tenths (denominator 10), the second is hundredths (denominator 100), and so on.

Why isn't 8.1 equal to 8 and 1/50?

Because $\frac{1}{50} = 0.02$ , not 0.1! Always check: what decimal does my fraction equal? Only $\frac{1}{10} = 0.1$ .

Do I need to simplify the fraction part?

Yes, always simplify! But $\frac{1}{10}$ is already in lowest terms since 1 and 10 share no common factors other than 1.

How can I double-check my mixed number is correct?

Convert it back to decimal! $8\frac{1}{10} = 8 + \frac{1}{10} = 8 + 0.1 = 8.1$ ✓

What if the decimal has more places, like 8.17?

Use the same method! $8.17 = 8 + 0.17 = 8 + \frac{17}{100} = 8\frac{17}{100}$ . The denominator matches the place value of the last digit.

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