# Ascending order

Objects that are grouped in ascending order are grouped from smallest to largest (from left to right). Objects such as shapes can be arranged in ascending order by size, while numbers listed in ascending order would start with the smallest number and end with the largest number. The bar graph below shows a set of numbers in ascending order.

Objects arranged in ascending order are arranged in the opposite way as objects in descending order (largest to smallest). There are many reasons to arrange objects in ascending, descending, or other orders. For example, it is necessary to arrange numbers to be able to find statistical values like the median, and mode.

## How to arrange numbers in ascending order

One way to arrange numbers is to think of them in terms of their position on a number line. Number lines are arranged such that numbers on the left are smaller and numbers on the right are larger. To list numbers in ascending order, read the number line from left to right, and order numbers in the same manner.

### Integers

To list a given set of integers in ascending order, identify the smallest and the largest integers first and write them on the ends. The smallest integer goes on the left, and the largest goes on the right. Leave enough space between the left-most and right-most integers. From there, compare the remaining integers to each other and fit them in their appropriate position between the smallest and largest integers.

Example

List the following set of integers in ascending order: 5, 12, 7, 19, 44, 62, 2

In the given set of numbers, 2 is the smallest integer and 62 is the largest, so they go on the ends. Then, comparing the size of the remaining integers, the set of numbers listed above in ascending order is:

2, 5, 7, 12, 19, 44, 62

### Fractions

To list fractions in ascending order, there are a few important things to remember.

- If the fractions being compared have the same denominators, the larger the numerator, the larger the value of the fraction.
- If the fractions being compared have the same numerators, the larger the denominator, the smaller the fraction.
- If fractions have different denominators and numerators, it is necessary to find a common denominator before comparing the sizes of their numerators.

Examples

List the following fractions in ascending order.

1. :

2. :

3. :

The least common denominator of this set of fractions is 30. Convert the fractions to equivalent fractions of 30:

List the fractions in ascending order:

Convert the fractions to their original forms:

### Decimals

Listing decimals in ascending order requires an understanding of how the decimal numeral system works. Each position in a number represents a power of 10. The further right of the decimal point, the smaller the value of the digit. The further left of the decimal point, the larger the value of the digit. Thus, 25.04 is smaller than 25.40, since the 4 in 25.04 is in the hundredths place, and the 4 in 25.40 is in the tenths place. Thus, more digits left of the decimal points means a larger number. If they have the same number of digits, the size of the digit in the corresponding positions need to be compared.

The same idea holds true to the right of the decimal point, except that decimal places that are further right represent smaller numbers. Thus, 25.300 is greater than 25.009.

Example

List the following numbers in ascending order: 1432.007, 10000, 2.512623462, 1432.1, 1432.10000007.

2.512623462, 1432.007, 1432.1, 1432.10000007, 10000