**Decimals**

Comparing and ordering decimals

- Comparing decimal is the process to identify if the decimal is greater or lesser or equal to another decimal.
- The sign used for comparing along with their meaning is shown in the table below:

Sign | Meaning |
---|---|

< | Less than |

> | Greater than |

= | Equal to |

Steps to compare decimals

Step 1: Compare the whole number first. The decimal with the bigger whole number is greater.

Step 2: If the whole number part is the same then compare the digits in the tenth place. The decimal with the greater tenth digit is bigger.

Step 3: If the digits in the tenth place are the same then compare the digits in the hundredth place. The decimal with the greater hundredth digit is bigger.

Step 4: If the digits are the same then keep moving to the digits on the right and compare them until you get a greater digit.

Examples:

Compare the decimals 23.567 and 23.586.

Solution:

Step 1: Start by comparing the whole number. The whole number on both the decimals is the same.

Step 2: On moving to the right of the decimals it is observed that the unequal digits are in the hundredth place.

Step 3: The decimal 23.567 has 6 in the hundredth place and the decimal 23.586 has 8 in the hundredth place.

Step 4: Since 6 < 8. Therefore, the decimal 23.567 is smaller than the decimal 23.586.

Hence, the answer is 23.567 < 23.586.

Steps to compare decimals using decimal place value chart

Step 1: Put the digits in the place value chart.

Step 2: Fill the empty squares in the place value chart with 0.

Step 3: Start comparing the digits in the place value chart from the left-hand side.

Step 4: If the digits are similar then compare the next digits until you get the different digits.

Step 5: The decimal with the greater digits is bigger.

Examples:

Compare the decimals 54.64 and 54.684.

Solution:

Step 1: Put each digit in the decimals place value chart.

Step 2: Fill the empty box with 0.

Step 3: Compare the digits starting from the extreme left side.

The digits in the hundredth place are unequal and also 8 > 4.

Therefore, 54.684 > 54.64.

Ordering decimals

Ascending order: means to arrange the given decimals from smaller to bigger.

Descending order: means to arrange the given numbers from bigger to smaller.

Examples 1:

Arrange the given decimals in ascending order.

64.478, 64.24, 64.357, 64.479

Solution:

The whole number part of all the decimals is the same. Therefore, compare the digits in the tenths, hundredths, and thousandths place. Arrange them from smaller to bigger.

The correct order is: 64.24, 64.357, 64.478, 64.479.

Examples 2:

Arrange the given decimals in descending order.

6.278, 46.14, 62.157

Solution:

Place each digit in the decimal place value chart, put 0 in the empty square and then start comparing the digits from the extreme left.

The correct order is: 62.157, 46.14, 6.278.

Representation of decimals on the number line

Let us understand how to mark the decimals on the number line.

Examples 1:

Mark 2.3 on the number line.

Solution:

Step 1: Draw a line segment marking 2 and 3.

Step 2: Divide the line segment 2 and 3 into ten equal parts.

Step 3: Count 3 steps from point 2 and mark it as 2.3.

Examples 2:

Mark 2.83 on the number line.

Solution:

Step 1: Draw a line segment marking 2.8 and 2.9.

Step 2: Divide the line segment into ten equal parts.

Step 3: Count 3 steps from point 2.8 and mark it as 2.83.

Common mistakes:

The students generally make mistakes in comparing by counting the total number of digits.