Convert 9.01: Decimal Representation Problem

Decimal Conversion with Hundredths Place

9.01= 9.01=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's convert the improper fraction into a mixed number.
00:09 First, break it down into a whole number, plus the remainder.
00:14 Next, change that remainder into a fraction.
00:21 Now, put it all together to form a mixed number.
00:26 And that's how we find the solution to the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

9.01= 9.01=

2

Step-by-step solution

Let's convert the decimal 9.019.01 into a mixed number step-by-step:

  • Step 1: Identify the integer part and the decimal part of 9.019.01.
    The integer part is 99 and the decimal part is 0.010.01.
  • Step 2: Convert the decimal part 0.010.01 to a fraction.
    0.010.01 is equivalent to 1100\frac{1}{100} because 0.010.01 means 1 part of 100 (i.e., hundredths).
  • Step 3: Form the mixed number using the integer part and the fractional part.
    Combine the integer part 99 with the fractional part 1100\frac{1}{100}:
    \9+1100=911009 + \frac{1}{100} = 9\frac{1}{100}.

Thus, the decimal 9.019.01 is equivalent to the mixed number 911009\frac{1}{100}.

Referring to the options provided, the correct answer is choice 4: 911009\frac{1}{100}.

Therefore, the solution to the problem is 911009\frac{1}{100}.

3

Final Answer

91100 9\frac{1}{100}

Key Points to Remember

Essential concepts to master this topic
  • Place Value Rule: Each decimal digit represents a specific fraction power
  • Technique: 0.01 means 1 hundredth = 1100 \frac{1}{100}
  • Check: Convert back: 91100=9+0.01=9.01 9\frac{1}{100} = 9 + 0.01 = 9.01

Common Mistakes

Avoid these frequent errors
  • Confusing tenths and hundredths place values
    Don't write 0.01 as 110 \frac{1}{10} = wrong denominator! This happens when you count decimal places incorrectly. Always remember: first decimal place is tenths, second is hundredths - so 0.01 means 1100 \frac{1}{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 if it's tenths or hundredths?

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Count the decimal places! One place after the decimal = tenths (0.1 = 110 \frac{1}{10} ). Two places = hundredths (0.01 = 1100 \frac{1}{100} ).

Why isn't 9.01 equal to 90 and 1/100?

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Because 9.01 has 9 whole units, not 90! The decimal point separates the whole number (9) from the decimal part (0.01). Don't let the zeros confuse you!

What's the difference between 9.01 and 9.10?

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9.01 = 91100 9\frac{1}{100} (1 hundredth), while 9.10 = 910100=9110 9\frac{10}{100} = 9\frac{1}{10} (10 hundredths = 1 tenth). The position matters!

Can I simplify the mixed number?

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In this case, 1100 \frac{1}{100} is already in simplest form because 1 and 100 share no common factors except 1. So 91100 9\frac{1}{100} is the final answer.

How do I convert back to check my work?

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Add the whole number and fraction: 9+1100=9+0.01=9.01 9 + \frac{1}{100} = 9 + 0.01 = 9.01 . If you get the original decimal, you're correct!

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