You can read tenths and hundredths. Cut a hundredth into 10 equal parts and you get a thousandth, the third place after the decimal point.
Key idea
After the decimal point the places are tenths, hundredths, thousandths. To read a decimal, read the whole number, say “and” for the point, read the digits after the point as one number, and finish with the name of the last place.
Why it works
$0.347$ is $\frac{3}{10} + \frac{4}{100} + \frac{7}{1000}$. Rename the tenths and hundredths as thousandths: $\frac{300}{1000} + \frac{40}{1000} + \frac{7}{1000} = \frac{347}{1000}$. That is why the whole decimal part can be read as “three hundred forty-seven thousandths.”
Worked examples
Worked example: Words to digits
Write “five and twelve thousandths” in digits.
- Five is the whole number: $5.\_\_\_$
- “Thousandths” means three places after the point, with the 12 ending in the thousandths place.
- So the places are 0 tenths, 1 hundredth, 2 thousandths.
Answer: $5.012$
Worked example: Expanded form
Write $4 \times 1 + 3 \times \frac{1}{10} + 8 \times \frac{1}{1000}$ as a decimal.
- 4 ones, 3 tenths and 8 thousandths.
- There are no hundredths, so the hundredths place gets a 0.
Answer: $4.308$
Common mistake
Leaving out a placeholder zero, like writing “five and twelve thousandths” as $5.12$. That is five and twelve hundredths. Check: the last digit must land in the place the last word names.