Convert Decimal 1.04: Finding All Equivalent Forms

Q: How do I know what power of 10 to use in the denominator?

Count the decimal places! For 1.04, there are 2 decimal places, so use 100 (which is 10²). One decimal place uses 10, two uses 100, three uses 1000, and so on.

Q: What if I can't find the greatest common divisor easily?

Start by listing factors! For $ \frac{4}{100} $, factors of 4 are: 1, 2, 4. Factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100. The greatest common factor is 4.

Q: Why do we need to simplify fractions?

Simplified fractions are in their simplest form and easier to work with. $ \frac{1}{25} $ is much clearer than $ \frac{4}{100} $, even though they're equal!

Q: How can I check if my mixed number is correct?

Convert it back to decimal! $ 1\frac{1}{25} = 1 + \frac{1}{25} $. Since $ \frac{1}{25} = 0.04 $, we get 1 + 0.04 = 1.04 ✓

Q: What's the difference between improper fractions and mixed numbers?

Mixed number: $ 1\frac{1}{25} $ shows whole part + fraction partImproper fraction: $ \frac{26}{25} $ has numerator larger than denominatorBoth represent the same value, just different formats!

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

00:07 Convert the remainder to fraction

00:13 Reduce the fraction, make sure to divide both numerator and denominator

00:27 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

$1.04=$

2

Step-by-step solution

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

Step 1: Identify the whole number and fractional parts of the decimal.
Step 2: Convert the fractional decimal to a fraction.
Step 3: Simplify the fraction to its lowest terms.
Step 4: Express the number as a mixed number.

Now, let's work through each step:

Step 1: The decimal given is $1.04$ . This can be broken down into a whole part and a fraction: $1 + 0.04$ .

Step 2: Convert the fractional part. We see $0.04$ as a fraction: $0.04 = \frac{4}{100}$ .

Step 3: Simplify the fraction. To simplify $\frac{4}{100}$ , we divide both the numerator and the denominator by their greatest common divisor, which is $4$ : $\frac{4}{100} = \frac{4 \div 4}{100 \div 4} = \frac{1}{25}$ .

Step 4: Combine this with the whole number. The mixed number is: $1 + \frac{1}{25} = 1\frac{1}{25}$ .

Therefore, the solution to the problem is $1\frac{1}{25}$ .

3

Final Answer

$1\frac{1}{25}$

Key Points to Remember

Essential concepts to master this topic

Rule: Place decimal digits over appropriate power of 10
Technique: Convert 0.04 to $\frac{4}{100}$ , then simplify by dividing by GCD
Check: Verify $1\frac{1}{25} = 1 + \frac{1}{25} = 1.04$ ✓

Common Mistakes

Avoid these frequent errors

Not simplifying the fraction to lowest terms
Don't leave $\frac{4}{100}$ unsimplified = $1\frac{4}{100}$ instead of the correct answer! This fraction can be reduced by dividing both numerator and denominator by their GCD of 4. Always simplify fractions by finding the greatest common divisor and dividing both parts.

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 what power of 10 to use in the denominator?

+

Count the decimal places! For 1.04, there are 2 decimal places, so use 100 (which is 10²). One decimal place uses 10, two uses 100, three uses 1000, and so on.

What if I can't find the greatest common divisor easily?

+

Start by listing factors! For $\frac{4}{100}$ , factors of 4 are: 1, 2, 4. Factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100. The greatest common factor is 4.

Why do we need to simplify fractions?

+

Simplified fractions are in their simplest form and easier to work with. $\frac{1}{25}$ is much clearer than $\frac{4}{100}$ , even though they're equal!

How can I check if my mixed number is correct?

+

Convert it back to decimal! $1\frac{1}{25} = 1 + \frac{1}{25}$ . Since $\frac{1}{25} = 0.04$ , we get 1 + 0.04 = 1.04 ✓

What's the difference between improper fractions and mixed numbers?

+

Mixed number: $1\frac{1}{25}$ shows whole part + fraction part
Improper fraction: $\frac{26}{25}$ has numerator larger than denominator
Both represent the same value, just different formats!

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Convert Decimal 1.04: Finding All Equivalent Forms

Decimal to Fraction Conversion with Simplification

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