What is the Ascending Order?
Arranging numbers from the smallest to the largest in an increasing order gives the ascending order. Here is an example.
As you can see, the smallest number is written first and then followed by the numbers that are larger than the previous number. In order to arrange numbers in ascending order, we need to compare them first and then arrange them in an increasing order.
The terms used to express values in ascending order are generally in an increasing order as seen earlier, or from the lowest to the highest value, or simply stated from the ‘bottom value’ to the ‘topmost value’.
How to Arrange Numbers in Ascending Order?
We can arrange numbers in ascending order by first comparing them with each other to identify the smallest number. Then the arrangement is done from the smallest to the number greater than the previous one. Now if there are three-digit or four-digit numbers that need to be arranged in ascending order, we will first compare the first digit of the numbers to identify the smallest digit. If the first digits of the numbers are the same, we will compare the second digits and move to the next digits if needed.
For example, to compare three digit numbers 456 and 465, we will start with comparing the first digits of the numbers. Here both have 4 as the first digit, Then we will compare the second digits of both, which are 5 and 6. Since 5 is less than 6, the number containing 5 as a second digit will be smaller than other, that is 456 < 465.
How to Arrange Fractions in Ascending Order?
There are three cases in which the factions can be arranged in ascending order.
- Arranging fractions with the same denominators:
When fractions have the same denominator, the fraction with the smallest numerator is regarded as the smallest fraction among them. For example, \(\frac{4}{7}, \frac{9}{7}, \frac{2}{7}, \frac{8}{7}\) have the same denominators. Compare the numerators and arrange them. Hence, the ascending order for this arrangement is, \(\frac{2}{7} < \frac{4}{7} < \frac{8}{7} < \frac{9}{7}.\)
- Arranging fractions with same numerators:
Fractions having the same numerators are arranged with the highest denominator being the smallest. For example, \(\frac{5}{7}, \frac{5}{2}, \frac{5}{4}, \frac{5}{9}\) have the same numerators. Now, compare the denominators in this case. As you can see,2 < 4 < 7 < 9, hence the arrangement in ascending order will be, \(\frac{5}{9} < \frac{5}{7} < \frac{5}{4} < \frac{5}{2}.\)
- Arranging fractions with different numerators and denominators:
In this case, the fractions are converted to like fractions(same denominators). Now we can arrange in ascending order by comparing their numerators.
How to Arrange Decimals in Ascending Order?
In order to arrange decimals in ascending order, we will first compare the whole number part of the decimal. The decimal number with a smallest whole number is regarded as the smallest. If the whole number parts are similar, we will compare the decimal parts as we did for the whole number parts.
Solved Examples
Example 1:
Arrange the following numbers in ascending order.
567, 22, 988, 10, 59, 480, 63, 490.
Solution:
To arrange the numbers in ascending order, the smallest number will be placed first and then followed by the number that is larger.
Hence, the arrangement will be 10, 22, 59, 63, 480, 490, 567, 988.
Example 2:
Margaret is arranging her books according to the length of each book. The lengths of her books are 5.6 inches, 8.9 inches, 6 inches, 7.5 inches, 9 inches, and 5.8 inches. Can you help her arrange the books in ascending order of their length?
Solution:
As we can see, the lengths of the books are in decimal forms. Hence, we will compare the whole number parts first to arrange the numbers in ascending order.
The numbers are 5.6, 8.9, 6, 7.5, 9, 5.8
The smallest whole number among them is 5 but there are two decimals with the same whole number. So, move to the decimal part. By comparing the decimal part, 5.6 < 5.8. Now arrange the other decimals:
5.6 < 5.8 < 6 < 7.5 < 8.9 < 9
Example 3:
Arrange the following fractions in ascending order.
\(\frac{3}{5}, \frac{2}{5}, \frac{9}{5}, \frac{8}{5}\).
Solution:
The denominators of all the fractions are the same. Hence, compare the numerators and arrange the fractions in ascending order.
Thus, the arrangement will be, \(\frac{2}{5} < \frac{3}{5} < \frac{8}{5} < \frac{9}{5}\).
The symbols used are ‘<’ (less than) and ‘>’ (greater than) for arranging numbers in ascending and descending order.
Zero is the smallest whole number.
No, all positive numbers are always greater than negative numbers.
The smaller number is always written to the left of the sign ‘<’.