Whole numbers are perfect for counting discrete objects like apples, chairs, and books. But when measuring continuous quantities like length, weight, or temperature, real objects rarely end exactly on a whole number mark.
To measure with absolute precision, we divide one whole unit into ten equal parts. Each part is called one-tenth ($\frac{1}{10}$). Written as a decimal, this is: $$0.1$$
If we slice each tenth into ten further sub-slices, the whole unit is divided into one hundred equal parts. Each tiny slice is one-hundredth ($\frac{1}{100}$), written as: $$0.01$$
Just as whole number places increase by $10$ times as you move leftward, places decrease by $\div 10$ as you move rightward across the decimal point:
| Hundreds ($100$) | Tens ($10$) | Ones ($1$) | Decimal Point (.) | Tenths ($\frac{1}{10} = 0.1$) | Hundredths ($\frac{1}{100} = 0.01$) | Thousandths ($\frac{1}{1000} = 0.001$) |
|---|---|---|---|---|---|---|
| $2$ | $5$ | $4$ | . | $3$ | $8$ | $5$ |
Expanded Form of $254.385$:
$$254.385 = (2 \times 100) + (5 \times 10) + (4 \times 1) + \left(3 \times \frac{1}{10}\right) + \left(8 \times \frac{1}{100}\right) + \left(5 \times \frac{1}{1000}\right)$$
Or in decimal expansion: $$254.385 = 200 + 50 + 4 + 0.3 + 0.08 + 0.005$$
Example: Write as a decimal: "Seven hundred five and thirty-six hundredths"
Whole Number Part: Seven hundred five $= 705$
Fractional Part: $36$ hundredths $= \frac{36}{100} = \frac{3}{10} + \frac{6}{100} = 0.36$
Complete Decimal: $\mathbf{705.36}$
Reading $12.35$ as "Twelve point thirty-five" is mathematically incorrect!
Digits after the decimal point do not have tens or hundreds values. $3$ is in the tenths place and $5$ is in the hundredths place. Correct reading: "Twelve point three five".
In digital medical thermometers, body temperature of $98.6^\circ\text{F}$ is healthy, but $101.4^\circ\text{F}$ indicates a high fever. That single tenth of a degree carries vital clinical information.