Convert Decimal 16.4 to Simplified Imaginary Fraction

Q: How do I know what denominator to use for the decimal part?

Count the digits after the decimal point! One digit means denominator is 10, two digits means 100, and so on. For 16.4, there's one digit (4), so use 10.

Q: What if I can't figure out how to simplify the fraction?

Find the Greatest Common Divisor (GCD) of the numerator and denominator. For $ \frac{4}{10} $, both 4 and 10 can be divided by 2, so $ \frac{4÷2}{10÷2} = \frac{2}{5} $.

Q: Why do I need to simplify fractions anyway?

Simplified fractions are easier to work with and represent the most reduced form of the number. It's like cleaning up your answer to make it as clear as possible!

Q: Can I convert mixed numbers back to decimals to check my work?

Absolutely! Divide the numerator by denominator: $ 2 ÷ 5 = 0.4 $, then add to the whole number: $ 16 + 0.4 = 16.4 $. Perfect check!

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

Same process! For example, 12.75 becomes $ 12 + \frac{75}{100} $. Then simplify: $ \frac{75}{100} = \frac{3}{4} $, so the answer is $ 12\frac{3}{4} $.

Decimal Conversion with Fraction Simplification

Convert into a mixed fraction:

$16.4$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Write as a reduced mixed fraction

00:03 Divide each digit after the decimal point by the division quantity it represents

00:09 Place the appropriate denominator

00:12 Remember to add 16

00:15 Reduce as much as possible, make sure to divide both numerator and denominator

00:33 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert into a mixed fraction:

$16.4$

Step-by-step solution

Let's write the decimal fraction as a mixed fraction.

Since there is one digit after the decimal point, we divide 4 by 10 and add 16, as follows:

$16+\frac{4}{10}$

Now let's divide the simple fraction by the highest number that can divide both the numerator and denominator, in this case the number is 2:

$16+\frac{4:2}{10:2}=16+\frac{2}{5}=16\frac{2}{5}$

Final Answer

$16\frac{2}{5}$

Key Points to Remember

Essential concepts to master this topic

Decimal Rule: Position after decimal determines denominator power of 10
Technique: Convert 16.4 = 16 + 4/10, then simplify by dividing by 2
Check: Convert back: 16 2/5 = 16.4 when 2÷5 = 0.4 ✓

Common Mistakes

Avoid these frequent errors

Not simplifying the fractional part
Don't leave 4/10 unsimplified = 16 4/10 instead of proper mixed number! This gives an incorrect final answer that isn't in simplest form. Always find the GCD and divide both numerator and denominator to get the simplest fraction.

Practice Quiz

Test your knowledge with interactive questions

Reduce the following fraction:

$$ 0.30 $$

FAQ

Everything you need to know about this question

How do I know what denominator to use for the decimal part?

Count the digits after the decimal point! One digit means denominator is 10, two digits means 100, and so on. For 16.4, there's one digit (4), so use 10.

What if I can't figure out how to simplify the fraction?

Find the Greatest Common Divisor (GCD) of the numerator and denominator. For $\frac{4}{10}$ , both 4 and 10 can be divided by 2, so $\frac{4÷2}{10÷2} = \frac{2}{5}$ .

Why do I need to simplify fractions anyway?

Simplified fractions are easier to work with and represent the most reduced form of the number. It's like cleaning up your answer to make it as clear as possible!

Can I convert mixed numbers back to decimals to check my work?

Absolutely! Divide the numerator by denominator: $2 ÷ 5 = 0.4$ , then add to the whole number: $16 + 0.4 = 16.4$ . Perfect check!

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

Same process! For example, 12.75 becomes $12 + \frac{75}{100}$ . Then simplify: $\frac{75}{100} = \frac{3}{4}$ , so the answer is $12\frac{3}{4}$ .

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