Convert Mixed Number 2 3/20 to an Improper Fraction

Mixed Number Conversion with Decimal Equivalence

2320= 2\frac{3}{20}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Let's change the number into a decimal fraction.
00:07 First, separate it into a whole number and a fraction.
00:11 We need the bottom part, or denominator, to be a multiple of ten.
00:17 Be sure to multiply both the top, the numerator, and the bottom, the denominator.
00:23 Next, convert it into a decimal fraction.
00:32 Then, add them together.
00:35 And that's how we solve the problem!

Step-by-step written solution

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1

Understand the problem

2320= 2\frac{3}{20}=

2

Step-by-step solution

To convert the mixed number 23202\frac{3}{20} to a decimal, we'll focus on converting the fractional part 320\frac{3}{20} first. We want to express it with a denominator of 100, because converting to tenths or hundredths makes it easier to switch to a decimal.

Step 1: Convert 320\frac{3}{20} to have a denominator of 100.

To get a denominator of 100, we find a factor that, when multiplied by 20, gives 100:

20×5=100 20 \times 5 = 100

So, we multiply both the numerator and the denominator of 320\frac{3}{20} by 5:

3×520×5=15100 \frac{3 \times 5}{20 \times 5} = \frac{15}{100}

Step 2: Convert 15100\frac{15}{100} to a decimal. Since 15100\frac{15}{100} is equivalent to 0.15:

15100=0.15 \frac{15}{100} = 0.15

Step 3: Combine with the whole number. The original number 23202\frac{3}{20} becomes:

2+0.15=2.15 2 + 0.15 = 2.15

Therefore, the decimal form of 23202\frac{3}{20} is 2.15\mathbf{2.15}.

3

Final Answer

2.15 2.15

Key Points to Remember

Essential concepts to master this topic
  • Method: Convert fraction part first, then add whole number
  • Technique: Find equivalent fraction with denominator 100: 320=15100=0.15 \frac{3}{20} = \frac{15}{100} = 0.15
  • Check: Verify by converting back: 2.15 = 2 + 0.15 = 215100=2320 2\frac{15}{100} = 2\frac{3}{20}

Common Mistakes

Avoid these frequent errors
  • Adding the fraction directly to decimal without conversion
    Don't add 2 + 3/20 = 2.3/20 = wrong answer! This treats the fraction as whole numbers instead of a decimal value. Always convert the fraction to decimal first: 3/20 = 0.15, then add 2 + 0.15 = 2.15.

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

\( 0.38= \)

FAQ

Everything you need to know about this question

Why do I need to convert to a denominator of 100?

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Converting to denominator 100 makes it super easy to write as a decimal! Since 100 = 10², fractions with denominator 100 directly become hundredths in decimal form.

What if the denominator doesn't go into 100 evenly?

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You can still convert! Try denominators like 10, 1000, or 10000. Or use long division: divide the numerator by the denominator to get the decimal directly.

How do I know if 2.15 is really equal to the mixed number?

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Convert back to check! 2.15=2+0.15=2+15100=215100 2.15 = 2 + 0.15 = 2 + \frac{15}{100} = 2\frac{15}{100} . Then simplify: 15100=320 \frac{15}{100} = \frac{3}{20} , so you get 2320 2\frac{3}{20}

Can I just divide 3 by 20 on a calculator?

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Yes! That's actually the quickest method. 3 ÷ 20 = 0.15, then add the whole number: 2 + 0.15 = 2.15. Both methods work perfectly!

Why isn't the answer 2.3 or 2.30?

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2.3 would mean 2310 2\frac{3}{10} , not 2320 2\frac{3}{20} ! The denominator matters. Since 320=0.15 \frac{3}{20} = 0.15 , not 0.3, the correct answer is 2.15.

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