Place value and ordering decimals

Decimal place values

We use a decimal point to separate units from parts of a whole, such as tenths, hundredths, thousandths, etc.

  • {0.1} is a tenth, \frac{1}{10}, of a unit
  • {0.01} is a hundredth, \frac{1}{100}, of a unit
  • {0.001} is a thousandth, \frac{1}{1,000}, of a unit

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}?

Table to compare the two decimals: 2.301 and 2.32

Both numbers have two units 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

Q1. In the number 3.546, what is the value of the digit 4?

Q2. Place the following numbers in order, smallest first: 3.2, 3.197, 3.02, 3.19

A1. The value of the digit 4 is four hundredths, or \frac{4}{100}.

A2. Did you get 3.02, 3.19, 3.197, 3.2?

All the numbers have three units, 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.