Converting Decimal to Fraction: Transform 0.55 into Simplified Form

Decimal to Fraction with Place Value

Convert 0.55 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
00:11 We moved the point twice to the right, so we'll add two 0s to the denominator
00:14 Write the digits in the numerator
00:18 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

Convert 0.55 into a fraction.

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the decimal number given as 0.55.
  • Step 2: Express 0.55 as a fraction using its place value.
  • Step 3: Verify which choice this corresponds to among the provided options.

Let's work through each step:

Step 1: We have the decimal 0.55.

Step 2: In the decimal number 0.55, the first '5' is in the tenths place, and the second '5' is in the hundredths place, so this can be expressed as:
0.55=55100 0.55 = \frac{55}{100} This places 55 over 100 to correspond with its placement in the hundredths position in decimal terminology.

Step 3: Comparing the resulting fraction 55100\frac{55}{100} with the choices provided, this matches choice number two. Therefore, choice number two is the correct answer.

Hence, the solution to the problem is 55100 \frac{55}{100} .

3

Final Answer

55100 \frac{55}{100}

Key Points to Remember

Essential concepts to master this topic
  • Place Value Rule: Use decimal position to determine denominator
  • Technique: 0.55 = 55/100 since last digit is hundredths place
  • Check: Verify 55/100 = 0.55 by dividing 55 ÷ 100 ✓

Common Mistakes

Avoid these frequent errors
  • Using wrong denominator based on digit count
    Don't use 10 just because there are 2 digits = 55/10 = 5.5, not 0.55! This ignores place value completely. Always use the place value of the rightmost digit to determine the denominator.

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?

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Look at the rightmost decimal place! If it's tenths, use 10. If it's hundredths, use 100. If it's thousandths, use 1000. For 0.55, the last 5 is in hundredths place, so use 100.

Why isn't 55/10 correct for 0.55?

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Because 5510=5.5 \frac{55}{10} = 5.5 , not 0.55! The denominator must match the place value of the rightmost digit, not just any power of 10.

Do I need to simplify 55/100?

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The question asks to convert to a fraction, and 55100 \frac{55}{100} is correct. However, you could simplify it to 1120 \frac{11}{20} by dividing both by 5.

What if there are zeros after the decimal?

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Count them too! For example, 0.050 would be 501000 \frac{50}{1000} because the rightmost digit is in the thousandths place.

How can I check if my fraction equals the original decimal?

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Divide the numerator by the denominator using long division or a calculator. For 55100 \frac{55}{100} : 55 ÷ 100 = 0.55 ✓

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