Skill: Relate decimals and mixed numbers

A terminating decimal has a whole-number part and a fractional part.

To change a decimal to a mixed number:

1. Keep the digits to the left of the decimal point as the whole-number part.
2. Write the digits to the right of the decimal point as a fraction.
3. Use a denominator based on the place value:
   • tenths $\rightarrow 10$
   • hundredths $\rightarrow 100$
   • thousandths $\rightarrow 1000$
4. Simplify the fraction if possible.

Example: Write $4.35$ as a mixed number.

The whole-number part is $4$.

The digits $35$ are in the hundredths place, so the fractional part is $\frac{35}{100}$:

$$4.35=4\frac{35}{100}$$

Now simplify $\frac{35}{100}$. Both $35$ and $100$ can be divided by $5$:

$$\frac{35}{100}=\frac{7}{20}$$

Therefore,

$$\boxed{4.35=4\frac{7}{20}}$$

The denominator is $100$ before simplifying because $0.35$ means $35$ hundredths. The digits do not form a fraction by themselves; their place value tells you the denominator.

To check the reverse conversion, convert $\frac{7}{20}$ to hundredths:

$$\frac{7}{20}=\frac{35}{100}=0.35$$

So $4\frac{7}{20}$ and $4.35$ represent the same quantity.