16.6 as a fraction

Understand the Problem

The question is asking how to convert the decimal number 16.6 into a fraction. This involves separating the whole number part from the decimal part and expressing it as a fraction.

Answer

The decimal number $16.6$ can be expressed as the fraction $\frac{83}{5}$ or the mixed number $16 \frac{3}{5}$.

Steps to Solve

Separate Whole Number and Decimal Part

First, we identify the whole number part and the decimal part of the number 16.6.

The whole number part is $16$.
The decimal part is $0.6$.

Convert the Decimal Part to a Fraction

Next, we convert the decimal part $0.6$ to a fraction.

Since $0.6$ can be expressed as $\frac{6}{10}$ (because there is one digit after the decimal point).

Simplify the Fraction

Now we simplify the fraction $\frac{6}{10}$.

The greatest common divisor (GCD) of $6$ and $10$ is $2$.
Dividing both the numerator and the denominator by $2$ gives us:

$$ \frac{6 \div 2}{10 \div 2} = \frac{3}{5} $$

Combine Whole Number and Fraction

Now we combine the whole number $16$ and the simplified fraction $\frac{3}{5}$.

This can be expressed as a mixed number:

$$ 16 \frac{3}{5} $$

Alternatively, if you want to express it as an improper fraction:

$$ \frac{16 \times 5 + 3}{5} = \frac{80 + 3}{5} = \frac{83}{5} $$

The decimal number 16.6 can be expressed as the fraction $\frac{83}{5}$ or as the mixed number $16 \frac{3}{5}$.

More Information

Converting decimal numbers to fractions is often useful in various mathematical applications, including simplifying calculations and enhancing understanding of number relationships. The process involves understanding place values and simplifying fractions.

Tips

Confusing the decimal part with the whole number part when converting.
Forgetting to simplify the fraction, which can lead to a more complex answer than necessary.
Not correctly identifying the GCD when simplifying.

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