Hundredths
Hundredths is the second decimal place value, representing one part out of one hundred equal parts.
Formula
1 \text{ hundredth} = \frac{1}{100} = 0.01
Definition
Hundredths is the second place after the decimal point: one hundredth ($0.01$) means $1$ out of $100$ equal pieces, and money uses hundredths naturally, one cent is one hundredth of a dollar. Formally, the hundredths place represents a digit multiplied by $10^{-2} = 0.01$; financial amounts are typically rounded to the nearest hundredth (the nearest cent), and since a percent is defined as a ratio per $100$, hundredths are the natural decimal representation of percentages. In floating-point arithmetic, numbers are not stored with infinite precision, so "hundredths" in a computer are really binary approximations, since $\$0.01$ has a non-terminating binary expansion, causing accumulation of rounding errors in financial software.
Example
$0.47$ means $47$ hundredths, or $47/100$: forty-seven cents is $47$ hundredths of a dollar ($\$0.47$), which is also $47\%$, since "per cent" literally means "per hundred." $0.63 = 60/100 + 3/100 = 63/100 = 63\%$, and to round $3.478$ to the nearest hundredth, look at the thousandths digit ($8 \ge 5$) and round up to $3.48$. In IEEE 754 double precision, $0.1 + 0.2 = 0.30000000000000004$, not $0.3$, because $0.1$ and $0.2$ have non-terminating binary expansions; financial software instead uses decimal arithmetic libraries or stores cents as integers to avoid this.
Key Insight
Hundredths and percents are the same thing: $47$ hundredths ($0.47$) is the same as $47$ percent ($47\%$), and this is not a coincidence, the second decimal place is literally the "per-hundred" position, which makes converting between decimals and percents as simple as shifting the decimal point two places. The imprecision of binary floating-point at the hundredths place is a practical reason why financial systems avoid floating-point entirely; the "Patriot missile bug" (1991) was caused by floating-point time accumulation error at the millisecond level, a real-world consequence of decimal/binary place-value mismatch.