# 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.

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

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

#### Steps to Solve

1. 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 $0.6$.
1. 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).
1. 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:

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

1. 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 $16 \frac{3}{5}$.

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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