Place and Place Values after the Decimal Point (Definition, Types and Examples) - BYJUS

# Place and Place Values after the Decimal Point

The digits on the left side of a decimal point represent the whole number part of the number, and the digits on the right side of the decimal point represent the fractional part. We have place values on the right side of the decimal point, just like the place values of the whole number part. Learn the places and place values of the digits on the right side of the decimal point. ...Read MoreRead Less

## 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.