Convert tenths fractions to decimals

A fraction with denominator 10 represents tenths and is written in decimal notation by placing its numerator in the tenths place: $\frac{a}{10}=0.a$ for $0\le a\le9$ , with mixed numbers represented by a whole-number part and a tenths part. Place-value charts and number lines show that $0.3$ , $\frac{3}{10}$ , and three tenths name the same quantity; this scope does not include converting hundredths, thousandths, or arbitrary fractions to decimals.

Detailed Explanation: Convert tenths fractions to decimals

A fraction with denominator $10$ tells you that the number is made of tenths.

To write $\frac{a}{10}$ as a decimal:

Keep the whole-number part, if there is one.
Write the numerator in the tenths place, which is the first digit after the decimal point.

Example

Convert $3\frac{4}{10}$ to a decimal.

The whole-number part is $3$ . The fraction $\frac{4}{10}$ means $4$ tenths, so write $4$ in the tenths place:

3\frac{4}{10}=3.4

Therefore, $3\frac{4}{10}$ is $3.4$ .

The numbers $3.4$ , $3\frac{4}{10}$ , and “3 wholes and 4 tenths” all name the same amount.

Learn by doing: Convert tenths fractions to decimals

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Decimal Concept Image - Picture and Fraction (10s) to Decimal - Tenths

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