Complete the Decimal Expression: 2.4 = ?

Decimal to Mixed Number Conversion

2.4= 2.4=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Convert to mixed fraction
00:03 Break down the number into whole number and remainder
00:08 Convert the remainder to a fraction
00:17 Reduce the fraction, make sure to divide both numerator and denominator
00:26 Add to mixed fraction
00:30 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

2.4= 2.4=

2

Step-by-step solution

To convert the decimal 2.42.4 into a mixed number, we'll follow these steps:

  • Step 1: Convert the decimal part 0.40.4 into a fraction.
  • Step 2: Simplify the fraction.
  • Step 3: Combine with the whole number.

Let's work through each step:
Step 1: Recognize that 0.40.4 means 410\frac{4}{10} because there is one digit after the decimal point, placing it into tenths.
Step 2: Simplify 410\frac{4}{10} by dividing both the numerator and denominator by their GCD, which is 2. This gives us 25\frac{2}{5}.
Step 3: Combine the whole number 22 with the fraction 25\frac{2}{5} to form the mixed number 2252\frac{2}{5}.

Therefore, the conversion of 2.42.4 to a mixed number is 225 2\frac{2}{5} .

3

Final Answer

225 2\frac{2}{5}

Key Points to Remember

Essential concepts to master this topic
  • Decimal Place Value: One decimal place means tenths position
  • Simplification: Reduce 410 \frac{4}{10} to 25 \frac{2}{5} by dividing by GCD of 2
  • Verification: Convert back: 225=2+25=2+0.4=2.4 2\frac{2}{5} = 2 + \frac{2}{5} = 2 + 0.4 = 2.4

Common Mistakes

Avoid these frequent errors
  • Not simplifying the fraction after conversion
    Don't leave 1410 1\frac{4}{10} as your final answer = incorrect! This fraction isn't in simplest form and doesn't match the whole number part. Always reduce fractions to lowest terms and verify the whole number is correct.

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

\( 0.38= \)

FAQ

Everything you need to know about this question

Why isn't 1410 1\frac{4}{10} correct if 0.4 equals 4/10?

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While 410 \frac{4}{10} does equal 0.4, you have the wrong whole number! The decimal 2.4 has a whole number part of 2, not 1. Plus, 410 \frac{4}{10} should be simplified to 25 \frac{2}{5} .

How do I know when to simplify a fraction?

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Always simplify! Find the GCD (Greatest Common Divisor) of the numerator and denominator. For 410 \frac{4}{10} , the GCD is 2, so divide both parts by 2 to get 25 \frac{2}{5} .

What if the decimal has more than one digit after the decimal point?

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The same process works! Two decimal places = hundredths, three = thousandths, etc. For example: 3.25=325100=314 3.25 = 3\frac{25}{100} = 3\frac{1}{4} after simplifying.

How can I check if my mixed number is correct?

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Convert it back to a decimal! Divide the fraction part and add to the whole number. For 225 2\frac{2}{5} : 2 ÷ 5 = 0.4, so 2 + 0.4 = 2.4

Why do we need mixed numbers when decimals are easier?

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Mixed numbers show the exact value without rounding! They're especially useful in cooking, construction, and when working with fractions in algebra. Both forms are valuable!

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