Apply the examples with Decimal Point Repair Game. Check the worked steps below, then practice on your own.
How to read digits after the point
Numbers shown after the decimal point are often easier to communicate one digit at a time. For 8.302, say “eight point three zero two.” Reading “three hundred two” after “point” can hide the place values and introduce ambiguity.
In technical settings, speak slowly and include every zero that appears before the final significant digit.
Leading zeros: the most common mistake
| Number | Say this |
|---|---|
| 0.05 | Zero point zero five |
| 0.005 | Zero point zero zero five |
| 12.007 | Twelve point zero zero seven |
| 0.0004 | Zero point zero zero zero four |
Each extra leading zero moves the nonzero digit one place to the right and makes the value ten times smaller.
Long decimals in calculator results
Some calculations produce repeating or long decimals: 1 ÷ 3 = 0.3333… and 1 ÷ 7 = 0.142857142857…. When reading a few displayed digits, state only those digits and identify the result as rounded or truncated if appropriate.
For example, a display of 0.14285714 is “zero point one four two eight five seven one four.” It is an approximation of 1/7, not an exact finite decimal representation.
Reading negative decimals
Read the minus sign first. −0.025 is “negative zero point zero two five.” The sign changes the direction on a number line but does not alter the positions of the decimal digits.
A subtraction such as 3 − 0.25 is different from a negative value written as −0.25; include the operation when describing a whole expression.
When scientific notation helps
Very small numbers may be easier to write and read with powers of ten. The number 0.000000001 is 1 × 10⁻⁹, commonly spoken as “one times ten to the minus ninth power.”
Scientific notation avoids a long chain of leading zeros and is particularly helpful in engineering, chemistry and calculator output.
Practice with mixed examples
- 0.0405: zero point zero four zero five.
- 7.0091: seven point zero zero nine one.
- −3.002: negative three point zero zero two.
- 0.00008: zero point zero zero zero zero eight.
Use the Decimal Point Repair Game to practice recognizing the correct position of the point and zeros.
Frequently asked questions
Do zeros after a decimal point matter?
Leading and interior zeros do: 0.05 and 0.5 differ by a factor of ten.
How do I read a repeating decimal?
Read the visible digits, then explain that the pattern repeats, such as 0.333… for one third.
Why does a calculator show e-9?
It is scientific notation for multiplication by 10 raised to the power −9.
Open the Decimal Point Repair Game, then explore Scientific Notation Calculator for more practice.