Decimals are another way to write tenths and hundredths. They extend the place-value chart you know from each place is ten times the next to the right of the ones.
Key idea
The first place after the decimal point is tenths; the second is hundredths. So $0.3 = \dfrac{3}{10}$, $0.03 = \dfrac{3}{100}$, and $0.47 = \dfrac{47}{100}$ (4 tenths and 7 hundredths). A whole number goes before the point: $2\dfrac{35}{100} = 2.35$.
Why it works
The places keep the same pattern: moving right, each place is one tenth of the place before it. One one splits into 10 tenths, and one tenth splits into 10 hundredths. The decimal point marks where the ones end, so each digit after it knows its size by its position.
Worked example: Hundredths only
Write $\dfrac{3}{100}$ as a decimal.
- There are 0 tenths and 3 hundredths.
- Put 0 in the tenths place and 3 in the hundredths place.
Answer: $0.03$
Worked example: With whole numbers
Write $4\dfrac{6}{10}$ as a decimal.
- The 4 goes before the decimal point.
- 6 tenths go in the first place after it.
Answer: $4.6$
Common mistake
Writing 3 hundredths as $0.3$ (that is 3 tenths, ten times as much), or 5 tenths as $0.05$. Read the last digit's place: in $0.03$ the 3 is in the hundredths place, so it says "3 hundredths."