Convert 1.11: Finding All Equivalent Representations

Decimal-to-Fraction Conversion with Hundredths

1.11= 1.11=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Let's convert this to a mixed fraction.
00:06 First, break down the number into a whole number and a remainder.
00:11 Next, change the remainder into a fraction.
00:17 Finally, combine to form a mixed fraction.
00:21 That's how you solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

1.11= 1.11=

2

Step-by-step solution

To solve the problem of converting 1.11 1.11 to a mixed number with a fraction, follow these steps:

  • Step 1: Identify the whole number and the decimal part in 1.11 1.11 . The whole number is 1 and the decimal part is 0.11.
  • Step 2: Convert the decimal part 0.11 0.11 into a fraction. Since 0.11 0.11 represents eleven hundredths, write it as 11100 \frac{11}{100} .
  • Step 3: Combine the whole number and the fraction to form the mixed number. The result is 111100 1 \frac{11}{100} .

Therefore, the solution to the problem is 111100 1\frac{11}{100} .

3

Final Answer

111100 1\frac{11}{100}

Key Points to Remember

Essential concepts to master this topic
  • Place Value: Each decimal place represents a specific fraction power
  • Technique: Convert 0.11 to 11100 \frac{11}{100} using hundredths place
  • Check: Verify 111100=1.11 1\frac{11}{100} = 1.11 by converting back ✓

Common Mistakes

Avoid these frequent errors
  • Reading decimal places incorrectly
    Don't read 1.11 as 'one and eleven tenths' = 11110 1\frac{11}{10} ! The second digit after the decimal is hundredths, not tenths, giving you an improper fraction greater than 2. Always count decimal places: first is tenths, second is hundredths.

Practice Quiz

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How much of the whole does the shaded area (blue) represent?

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), two places = hundredths (0.01). In 1.11, there are two places, so it's eleven hundredths.

Why can't I simplify 11100 \frac{11}{100} ?

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Great question! Since 11 is a prime number and doesn't share any common factors with 100 (except 1), the fraction 11100 \frac{11}{100} is already in lowest terms.

What's the difference between 1.1 and 1.11?

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1.1 = 1110 1\frac{1}{10} (one tenth), while 1.11 = 111100 1\frac{11}{100} (eleven hundredths). The extra digit makes it a smaller increment!

How do I convert the mixed number back to check?

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Convert 111100 1\frac{11}{100} by keeping the whole number (1) and dividing: 11 ÷ 100 = 0.11. So 1 + 0.11 = 1.11 ✓

What if I have more decimal places?

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The same rule applies! Three places = thousandths, four places = ten-thousandths. Just count the digits after the decimal point to find your denominator.

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