Convert Decimal to Fraction: Finding the Fraction Equal to 0.07

Decimal Conversion with Hundredths Place

Convert 0.07 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 to the right until the number is whole
00:06 In a decimal fraction, the denominator must be some multiple of 10 and 10
00:09 We moved the point twice to the right, so we'll add two 0s to the denominator
00:15 Write the digits in the numerator
00:20 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 0.07 into a fraction.

2

Step-by-step solution

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

  • Step 1: Identify the decimal place value.
  • Step 2: Write the decimal as a fraction based on the place value.
  • Step 3: Check if the fraction can be simplified.

Now, let's work through each step:
Step 1: The given decimal is 0.07. The digit 7 is in the hundredths place, which indicates that the denominator should be 100.
Step 2: We write 0.07 as a fraction: 7100\frac{7}{100}.
Step 3: Check for simplification. The fraction 7100\frac{7}{100} is already in its simplest form since 7 is a prime number and cannot be divided further by 100.

Thus, the fraction form of 0.07 is 7100\frac{7}{100}.

Considering the multiple-choice options:

  • Choice 1: 710\frac{7}{10} - Incorrect, as this corresponds to the decimal 0.7.
  • Choice 2: 71000\frac{7}{1000} - Incorrect, as this corresponds to the decimal 0.007.
  • Choice 3: 7100\frac{7}{100} - Correct, as this matches the calculation we performed.
  • Choice 4: 70100\frac{70}{100} - Incorrect, as this can be simplified to 710\frac{7}{10}.

Therefore, the correct answer is 7100\frac{7}{100}, corresponding to choice 3.

3

Final Answer

7100 \frac{7}{100}

Key Points to Remember

Essential concepts to master this topic
  • Place Value: Decimal position determines the denominator (hundredths = 100)
  • Method: Write 0.07 as 7100 \frac{7}{100} using place value
  • Check: Verify by dividing: 7 ÷ 100 = 0.07 ✓

Common Mistakes

Avoid these frequent errors
  • Using wrong denominator based on digit count
    Don't count digits to get denominator like 710 \frac{7}{10} = wrong decimal 0.7! This ignores the actual decimal place value. Always use the place value: hundredths means denominator 100.

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 which denominator to use?

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Look at the rightmost digit's place value! If it's in the tenths place, use 10. If it's in the hundredths place (like 0.07), use 100. If it's in the thousandths place, use 1000.

Why isn't the answer 7/10?

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Because 710 \frac{7}{10} equals 0.7, not 0.07! The zero after the decimal point matters - it shows that 7 is in the hundredths place, not the tenths place.

Do I need to simplify the fraction?

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Check if you can! For 7100 \frac{7}{100} , since 7 is prime and doesn't divide into 100, it's already in simplest form.

What if I get confused about place values?

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Write out the place value chart: tenths, hundredths, thousandths. Count the decimal places from left to right. 0.07 has the 7 in the second place = hundredths = 100.

How can I check my answer?

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Divide the numerator by denominator: 7 ÷ 100 = 0.07. If this matches your original decimal, you're correct!

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