Decimals - Decimals as Fractions

Decimals are another way of expressing fractions that have denominators like $10, 100, 1000$, etc. A decimal point is used to separate the whole number part from the fractional part. For example, in $4.5$, $4$ is the whole number and $.5$ is the fractional part.

The Tenths Place: When a whole object is divided into 10 equal parts, each part is called one-tenth. Visually, imagine a rectangular bar divided into 10 equal vertical columns. Shading one column represents $\frac{1}{10}$ or $0.1$. If you shade 3 columns, it represents $\frac{3}{10}$ or $0.3$.

The Hundredths Place: When a whole is divided into 100 equal parts, each part is one-hundredth. Imagine a large square grid containing $10 \times 10$ small squares (100 total). Shading one tiny square represents $\frac{1}{100}$ or $0.01$. Shading 25 squares represents $\frac{25}{100}$ or $0.25$.

Place Value Relationship: In the decimal system, as we move from left to right, the value of each place becomes one-tenth of the previous place. The place to the right of the decimal point is the 'Tenths' ($1/10$) and the next place to the right is the 'Hundredths' ($1/100$).

Converting Decimals to Fractions: To convert a decimal to a fraction, look at the number of digits after the decimal point. If there is one digit, use $10$ as the denominator. If there are two digits, use $100$ as the denominator. For example, $0.8$ becomes $\frac{8}{10}$ and $0.09$ becomes $\frac{9}{100}$.

Mixed Decimals: A decimal that has a non-zero whole number part is called a mixed decimal. Visually, this looks like multiple fully shaded shapes plus a partially shaded shape. For example, $2.4$ represents 2 whole items and 4 tenths of a third item, which can be written as the mixed fraction $2 \frac{4}{10}$.

Reading Decimals: We read the decimal point as 'point'. For example, $15.72$ is read as 'fifteen point seven two'. Note that digits after the decimal point are always read individually ($seven\ two$, not $seventy-two$).