Convert 0.8 to a Simplified Fraction: Step-by-Step Solution

Decimal to Fraction with Simplification

Write the following decimal fraction as a simple fraction and simplify:

0.8 0.8

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Convert to a simple fraction and reduce as much as possible
00:03 Write the digits after the decimal point as a whole number
00:06 Count how many digits are after the decimal point to determine the denominator
00:09 There is only one digit, so the denominator will be 10
00:14 Divide the fraction by the greatest common factor
00:17 Make sure to divide both numerator and denominator
00:22 Calculate the quotients
00:25 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

Write the following decimal fraction as a simple fraction and simplify:

0.8 0.8

2

Step-by-step solution

Since there is one digit after the decimal point, we divide 8 by 10:

810 \frac{8}{10}

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 2, so:

8:210:2=45 \frac{8:2}{10:2}=\frac{4}{5}

3

Final Answer

45 \frac{4}{5}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Place decimal digits over power of 10 based on decimal places
  • Technique: 0.8 = 8/10, then divide by GCD of 2
  • Check: Verify 4/5 = 0.8 by dividing 4 ÷ 5 = 0.8 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to simplify the fraction
    Don't leave 8/10 as your final answer = incorrect simplified form! The fraction isn't in lowest terms and teachers expect simplification. Always find the GCD and divide both numerator and denominator by it.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

\( 5:6= \)

FAQ

Everything you need to know about this question

How do I know what power of 10 to use?

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Count the decimal places! One decimal place = divide by 10, two places = divide by 100, three places = divide by 1000, and so on.

What if I can't find the GCD easily?

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Start by checking if both numbers are even (divide by 2). Then try other small numbers like 3, 5, 7. You can also list all factors of each number and find the greatest common one.

How do I check if my fraction is fully simplified?

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A fraction is simplified when the numerator and denominator have no common factors except 1. If you can't divide both by the same number anymore, you're done!

Can I convert back to check my answer?

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Absolutely! Divide the numerator by denominator: 45=4÷5=0.8 \frac{4}{5} = 4 \div 5 = 0.8 . If you get your original decimal, you're correct!

What if the decimal has more than one digit?

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Same process! For example, 0.25 = 25100=14 \frac{25}{100} = \frac{1}{4} after dividing by GCD of 25.

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