Decimal place values
We use a decimal point to separate units (ones) from parts of a whole, such as tenths, hundredths, thousandths, etc.
- \({0.1}\) is a tenth, \(\frac{1}{10}\), of a one
- \({0.01}\) is a hundredth, \(\frac{1}{100}\), of a one
- \({0.001}\) is a thousandth, \(\frac{1}{1,000}\), of a one
In \({52.13}\), the value of the digit \({1}\) is one tenth or \(\frac{1}{10}\), and the value of the digit \(3\) is three hundredths or \(\frac{3}{100}\).
Ordering decimals
When ordering numbers, always compare the left digits first.
For example, which is greater \({2.301}\) or \({2.32}\)?
Both numbers have two ones and three tenths, but \({2.301}\) has no hundredths, whereas \({2.32}\) has two hundredths. Therefore, \({2.32}\) is greater than \({2.301}\).
Adding a zero
Another way to look at it is to add a zero to the end of \({2.32}\). This doesn't change the value as it is after the decimal point. This means that both numbers will have the same number of digits after the decimal point.
The two numbers are now \({2.320}\) and \({2.301}\). It is easier to see that \({2.320}\) is bigger - just as \({2,320}\) is bigger than \({2,301}\).
Question
In the number \(3.546\), what is the value of the digit \(4\)?
The value of the digit \(4\) is four hundredths, or \(\frac{4}{100}\).
Question
Place the following numbers in order, smallest first: \(3.2\), \(3.197\), \(3.02\), \(3.19\)
Did you get \(3.02\), \(3.19\), \(3.197\), \(3.2\)?
All the numbers have three ones, so start by comparing the tenths. \(3.02\) has no tenths, \(3.197\) and \(3.19\) have one tenth, and \(3.2\) has two tenths. Therefore, \(3.02\) is the smallest and \(3.2\) is the largest.
When comparing \(3.197\) and \(3.19\), both have \({9}\) hundredths. \(3.19\) has no further digits, but \(3.197\) also has \({7}\) thousandths, meaning that \(3.19\) is smaller than \(3.197\).
You can add zeros to the ends of the numbers and so write the numbers as \(3.020\), \(3.190\), \(3.197\) and \(3.200\) and compare them.