Decimal to Fraction Conversion: Transform 0.93 to Simplest Form

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

Look at the rightmost decimal place! If it's tenths (1 place), use 10. If it's hundredths (2 places), use 100. If it's thousandths (3 places), use 1000. The denominator is always a power of 10.

Q: Why isn't 93/100 simplified further?

To simplify fractions, you need common factors in both numerator and denominator. Since 93 = 3 × 31 and 100 = 2² × 5², they share no common factors, so $ \frac{93}{100} $ is already in simplest form!

Q: What if I wrote 930/1000 instead?

That's mathematically equal to $ \frac{93}{100} $, but it's not in simplest form. You can divide both top and bottom by 10 to get the correct simplified answer.

Q: Can I convert this fraction back to check my work?

Absolutely! Divide 93 ÷ 100 = 0.93. If you get back your original decimal, your fraction conversion is correct!

Decimal Conversion with Place Value Recognition

Convert 0.93 into a fraction.

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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

00:03 Move the decimal point right until the number is whole

00:06 In a decimal fraction, the denominator must be some multiple of 10 by 10

00:09 We moved the point twice to the right, so we'll add 2 zeros to the denominator

00:13 Write the digits in the numerator

00:17 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

Convert 0.93 into a fraction.

Step-by-step solution

To convert the decimal 0.93 into a fraction, observe the following steps:

Step 1: Recognize that 0.93 is in the hundredths place. Thus, it can be directly expressed as $\frac{93}{100}$ . The number 93 is the numerator, and 100 is the denominator, reflecting the decimal's position.
Step 2: Consider simplifying the fraction. Since 93 and 100 have no common factors other than 1, $\frac{93}{100}$ is already in its simplest form.
Step 3: Check if the fraction matches the multiple-choice options provided. In this case, $\frac{93}{100}$ is the correct choice.

Therefore, the decimal 0.93 is equivalent to the fraction $\frac{93}{100}$ .

Final Answer

$\frac{93}{100}$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Two decimal places means hundredths, so denominator is 100
Direct Method: 0.93 = 93/100 by reading place value position
Simplification Check: Find GCD of 93 and 100: no common factors = already simplified ✓

Common Mistakes

Avoid these frequent errors

Using wrong denominator based on decimal digits
Don't count digits and use 1000 as denominator for 0.93 = 93/1000! This ignores place value meaning. The last digit is in hundredths place, so denominator must be 100. Always use place value position, not digit count.

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

$$ 0.38= $$

FAQ

Everything you need to know about this question

How do I know what denominator to use for any decimal?

Look at the rightmost decimal place! If it's tenths (1 place), use 10. If it's hundredths (2 places), use 100. If it's thousandths (3 places), use 1000. The denominator is always a power of 10.

Why isn't 93/100 simplified further?

To simplify fractions, you need common factors in both numerator and denominator. Since 93 = 3 × 31 and 100 = 2² × 5², they share no common factors, so $\frac{93}{100}$ is already in simplest form!

What if I wrote 930/1000 instead?

That's mathematically equal to $\frac{93}{100}$ , but it's not in simplest form. You can divide both top and bottom by 10 to get the correct simplified answer.

Can I convert this fraction back to check my work?

Absolutely! Divide 93 ÷ 100 = 0.93. If you get back your original decimal, your fraction conversion is correct!

Do all decimals convert to simple fractions?

Terminating decimals (like 0.93) always convert to simple fractions. But repeating decimals (like 0.333...) need special techniques. For now, focus on terminating decimals like this problem!

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