Relate decimals and mixed numbers

A terminating decimal can be interpreted as a whole-number part plus a fractional part with a denominator based on powers of ten, and represented equivalently as a mixed number; the reverse conversion preserves the same quantity. Place value and number-line representations clarify relationships such as $4.35=4\frac{35}{100}=4\frac{7}{20}$ , avoiding the misconception that decimal digits form a numerator independently of their place value. Nonterminating-decimal conversions are outside this scope.

Detailed Explanation: 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:

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

Learn by doing: Relate decimals and mixed numbers

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Decimals to Fractions - Standard

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