Convert 0.58 to a Simplified Fraction: Step-by-Step Solution

Decimal Conversion with GCD Simplification

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

0.58 0.58

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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
00:07 Count how many digits are after the decimal point to determine the denominator
00:10 There are 2 digits after the decimal point, therefore the denominator will be 100
00:16 Divide the fraction by the greatest common factor
00:22 Make sure to divide both numerator and denominator
00:27 Calculate the numerator
00:31 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

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

0.58 0.58

2

Step-by-step solution

Since there are two digits after the decimal point, we divide 58 by 100:

58100 \frac{58}{100}

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

In this case, the number is 2, so:

58:2100:2=2950 \frac{58:2}{100:2}=\frac{29}{50}

3

Final Answer

2950 \frac{29}{50}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Place decimal digits over power of 10 matching decimal places
  • Technique: Convert 0.58 to 58100 \frac{58}{100} then find GCD
  • Check: Divide 29 by 50: 29 ÷ 50 = 0.58 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to simplify the fraction
    Don't leave 58100 \frac{58}{100} as your final answer = not in simplest form! This fraction can still be reduced by dividing both parts by their greatest common divisor. 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 to put in the denominator?

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Count the decimal places! For 0.58, there are 2 decimal places, so use 58100 \frac{58}{100} (100 = 10²). For 0.375, there are 3 places, so use 3751000 \frac{375}{1000} .

What's the fastest way to find the GCD?

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List the factors of both numbers or use the division method. For 58 and 100: factors of 58 are 1, 2, 29, 58 and factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. The largest common factor is 2.

Can I simplify before converting the decimal?

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No, you need to convert the decimal to a fraction first! You can't simplify 0.58 directly. Always convert to 58100 \frac{58}{100} first, then simplify to 2950 \frac{29}{50} .

How do I check if my simplified fraction is correct?

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Divide the numerator by the denominator! For 2950 \frac{29}{50} : 29 ÷ 50 = 0.58. If you get back your original decimal, you're right!

What if the decimal has more than 2 places?

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Same process! For 0.125 (3 decimal places), write 1251000 \frac{125}{1000} , then find GCD of 125 and 1000, which is 125, giving you 18 \frac{1}{8} .

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