Place and Place Values after the Decimal Point
Each digit after the decimal point has a name, just like each digit in a whole number has a name based on its place value. The names in the visual are in the same sequence as the whole number place value names but in the opposite direction. It is important to memorize these place value names so that you know how to round a number to a specific place value when required. Understanding these terms will also aid you in understanding fractions.
A comma (,) is used to group the numbers to the left of the decimal point for better readability. A period (.) is used for the decimal point. Decimals present a different way of representing fractions and mixed numbers that have denominators which are in the powers of ten; such as 10, 100, 1000, 10000, and so on.
For example, let us consider the decimal 0.7;
0.7 is the same as the fraction, \(\frac{7}{10}\)
The second digit to the right of the decimal point indicates the number of ‘hundredths’.
For example, the decimal
4.23
4.23 is the same as the mixed number \(4\frac{3}{13}\)
You can write decimals with different place values to the right of the decimal point. Let’s consider the number 87.458342. The numbers after the decimal point with their respective place values are named as follows.
To understand and visualize decimals, we can use blocks of base 10. Let’s assume that a large square is a whole unit. If this square is divided into 10 equal strips, each of these strips represents \(\frac{1}{10}\) or 0.1 and these strips represent one tenth of the whole. If one of these strips were cut into ten smaller pieces, it would represent \(\frac{1}{100}\) or 0.01 of the whole.
Solved Example
Example 1: What number does the following sets of diagrams represent?
In the diagram there are 9 strips. This means that ‘9’ comes under the tenth’s place. The last strip has three boxes that are coloured and each square represents the hundredth’s place. This means that the number represented in this scenario is 0.93.
Example 2:
The large square represents the ‘ones’ place. We can write one under the ‘ones’ place. One strip which represents the ‘tenths’ place is coloured. This means we can write one under the ‘tenths’ place. Lastly, 4 small squares are also coloured. The squares represent the hundredth’s place. The number represented in the scenario presented here is 1.14.
Example 3:
What number does the following set of blocks represent, if the squares represent the ‘units’ place, the strips represent the ‘tenths’ place and the smallest squares represent the ‘hundredths’ place?
Since the square represents the ‘units’ place and there are two squares, we can write 2 in the unit’s place. The strips represent the ‘tenths’ place. There are four strips , hence we can write ‘4’ in the ‘tenths’ place. Finally, there are ‘8’ small squares, hence ‘8’ can be written in the ‘hundredths’ place. Therefore, the number represented in this scenario is 2.49.
Example 4:
Timothy goes to a shopping mall that has a total of ten floors. Ten of these floors have enough space to accommodate 10 shops but the tenth floor only has three shops. Represent this scenario by shading the diagram given below.
There are a total of 10 strips and each strip represents one floor. Each small square represents one shop. Since nine of the floors are completely filled with shops, we can shade nine strips completely. In the last strip only three squares need to be coloured as only three shops are open.
A number having a lot of digits may not have a high numerical value as this depends on the number. A number that has a lot of digits on the right side of the decimal point need not be a number that has a high numeric value. For example the number 1 has a greater value than 0.67986688737.
Decimal points are used to determine the accurate weight of everyday objects. It is also used in stopwatches to determine the accurate time as decimal numbers give us accurate and precise values when compared to whole numbers.