Convert Decimal to Fraction: Simplifying 0.58 to Lowest Terms

Q: How do I know what power of 10 to use?

Count the decimal places! One decimal place means tenths (10), two places means hundredths (100), three places means thousandths (1000). Since 0.58 has two decimal places, use 100.

Q: What if I can't find the GCD easily?

Try dividing by small numbers like 2, 3, 5 first! For $ \frac{58}{100} $, both numbers are even, so divide by 2: $ \frac{29}{50} $. Since 29 is prime and doesn't divide 50, you're done!

Q: Can I convert 0.58 to a different fraction?

Yes, but $ \frac{29}{50} $ is the simplest form. You could write equivalent fractions like $ \frac{58}{100} $ or $ \frac{116}{200} $, but always reduce to lowest terms!

Q: How can I check if my fraction is fully simplified?

The fraction is fully simplified when the GCD of numerator and denominator is 1. For $ \frac{29}{50} $, since 29 is prime and doesn't divide 50, the GCD is 1.

Q: What if the decimal has more places, like 0.125?

Same process! 0.125 has three decimal places, so write $ \frac{125}{1000} $. Then find GCD (125) and simplify to get $ \frac{1}{8} $.

Decimal Conversion with Fraction Simplification

Write 0.58 as a fraction and reduce.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert to a simple and reduced fraction

00:03 Place the digits in the numerator

00:08 Move the decimal point right until the number is whole and not decimal

00:14 We moved 2 times, so the denominator will equal 100

00:17 Now let's reduce as much as possible

00:20 Break down 58 into factors 2 and 29, and 100 into factors 2 and 50

00:29 Reduce what we can

00:35 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

Write 0.58 as a fraction and reduce.

Step-by-step solution

To convert the decimal number 0.58 to a fraction:

Step 1: Write 0.58 as a fraction with a power of 10 in the denominator. Since there are two decimal places, we write it as:
$0.58 = \frac{58}{100}$
Step 2: Simplify the fraction. Find the greatest common divisor (GCD) of 58 and 100. The GCD is 2.
Step 3: Divide both the numerator and the denominator by their GCD to simplify:
$\frac{58}{100} = \frac{58 \div 2}{100 \div 2} = \frac{29}{50}$

Therefore, the decimal 0.58 expressed as a fraction in its simplest form is $\frac{29}{50}$ .

Final Answer

$\frac{29}{50}$

Key Points to Remember

Essential concepts to master this topic

Rule: Place decimal over power of 10 based on decimal places
Technique: 0.58 becomes $\frac{58}{100}$ then find GCD
Check: Divide 29 by 50 to get 0.58 back ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fraction after conversion
Don't leave $\frac{58}{100}$ as your final answer = not in lowest terms! This is still correct but not simplified. Always find the GCD and divide both numerator and denominator to get $\frac{29}{50}$ .

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 power of 10 to use?

Count the decimal places! One decimal place means tenths (10), two places means hundredths (100), three places means thousandths (1000). Since 0.58 has two decimal places, use 100.

What if I can't find the GCD easily?

Try dividing by small numbers like 2, 3, 5 first! For $\frac{58}{100}$ , both numbers are even, so divide by 2: $\frac{29}{50}$ . Since 29 is prime and doesn't divide 50, you're done!

Can I convert 0.58 to a different fraction?

Yes, but $\frac{29}{50}$ is the simplest form. You could write equivalent fractions like $\frac{58}{100}$ or $\frac{116}{200}$ , but always reduce to lowest terms!

How can I check if my fraction is fully simplified?

The fraction is fully simplified when the GCD of numerator and denominator is 1. For $\frac{29}{50}$ , since 29 is prime and doesn't divide 50, the GCD is 1.

What if the decimal has more places, like 0.125?

Same process! 0.125 has three decimal places, so write $\frac{125}{1000}$ . Then find GCD (125) and simplify to get $\frac{1}{8}$ .

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