Represent decimals to thousandths
Theory
The third place after the decimal point is thousandths, worth one part in a thousand. Reading right from the point the places are tenths, hundredths and thousandths, and a digit's value is the digit times its place.
A decimal shows parts of a whole using places after the point.
The first three places after the point are tenths \((0.1)\), hundredths \((0.01)\) and thousandths \((0.001)\).
The value of a digit is the digit multiplied by its place, so the \(6\) in \(0.006\) is worth \(0.006\). Zeros hold empty places and keep the other digits in the correct column.
Each place after the point is ten times smaller than the one before it.
| Place | Value | Example digit |
|---|---|---|
| Tenths | \(0.1\) | \(0.4 \rightarrow 0.4\) |
| Hundredths | \(0.01\) | \(0.04 \rightarrow 0.04\) |
| Thousandths | \(0.001\) | \(0.006 \rightarrow 0.006\) |
How to read a decimal to thousandths
- Name the places after the point in order: tenths, hundredths, thousandths.
- Read each digit's value as the digit times its place.
- Partition by adding the value of each non-zero digit.
The \(2\) is in the thousandths place.
| \(\text{value}\) | \(=\) | \(0.002\) |
Eighty-three thousandths means \(83\) out of \(1000\).
| \(83\text{ thousandths}\) | \(=\) | \(0.083\) |
Only the non-zero digits give a term.
| \(2.045\) | \(=\) | \(2 + 0.04 + 0.005\) |
There are 1000 mm in 1 m, so multiply by 1000.
| \(0.125 \times 1000\) | \(=\) | \(125\text{ mm}\) |
Common pitfalls
Frequently asked questions
What is the thousandths place?
It is the third place after the decimal point. One thousandth is written \(0.001\), one part of a whole split into a thousand equal parts.
How do you find the value of a digit?
Multiply the digit by its place. In \(6.052\) the \(2\) is in the thousandths place, so its value is \(0.002\).
Why do zeros matter in a decimal?
A zero holds a place so the other digits stay in the correct column. In \(3.006\) the two zeros keep the \(6\) in the thousandths place.
How do you write a decimal in words?
Read the whole-number part, then read the decimal part using the last place. \(0.083\) is eighty-three thousandths.