Ascending Order

Ascending order refers to the arrangement of numbers or items in an increasing order from the smallest to the largest. A common example of ascending order can be seen on a number line as we read the numbers from left to right. Numbers can be arranged in ascending order by putting commas between numbers or by using the 'less-than symbol (<)' between numbers. For example, 1, 2, 3, 4, 5 or 1 < 2 < 3 < 4 < 5.

Have you ever come across situations where you have so many important folders/files/documents that may be useful to you, but because they are so many in number, you can't find the correct one? Well, most of such problems can be solved if you arrange them in some particular pattern or order. Arranging things in ascending order is one way to collect and represent data.

Ascending means increasing. So when any quantity/map/list has its values from smallest to largest, we say that it is an ascending quantity/map/list. This increase can be in any form such as alphabets, weights, heights, and time. For example, we say, 'The rocket is ascending into the sky.' Here, it means that the rocket's distance from the ground after lift-off is constantly ascending as it orbits into space. This was a general idea for the word 'ascending.' Now, let us try to narrow down our knowledge to 'ascending order.'

What is Increasing Order?

The arrangement of data from the smallest to the largest value is known as ascending order. It is also known as increasing order. For example, consider the following numbers: [6,2,8,4,0]. Now, let us try to arrange them in an increasing order. Thus, we get:

Hence, the above numbers are arranged in ascending order as [0, 2, 4, 6, 8] or 0 < 2 < 4 < 6 < 8. While arranging a given set of numbers in ascending order, there are a few rules that we need to keep in our mind. These rules are listed below:

• The first value is always the smallest.
• The values should always be in order from smallest to largest.
• The last value is always the largest.

For example, in the ascending arrangement: [49, 54, 89, 623, 810],

• The number 49 is the smallest, hence the first one on the list.
• The number 810 is the largest, hence the last one on the list.

To represent a given set of numbers in ascending order, we can either put commas ',' or we can use the 'less than symbol (<)'. The most common way to represent numbers in ascending order is by putting a less than symbol in between, which shows that the number on the left is smaller in value than the number on the right side of the symbol. For example, 2 < 3 < 4 are arranged in ascending order.

Ascending order of fractions means arranging the given fractions in increasing order. In the case of fractions, there are two ways to arrange them into increasing order and those are listed below:

Method 1

By converting fractions to decimals

We can convert fractions to decimals by dividing the numerator with the denominator, and then we can arrange those decimals into ascending order by looking at the whole number part and the decimal part place values. Let us understand this with the help of an example.

Example: Arrange the following fractions in ascending order: 1/2, 2/5, 5/6, 3/5

Solution: If we convert these fractions into their decimal equivalents one by one, we get,

1/2 = 0.5

2/5 = 0.4

5/6 = 0.83

3/5 = 0.6

Now, all these decimals have 0 in the whole number part, so we need to look at the digit at the tenths place to arrange these numbers in ascending order.

0.4 < 0.5 < 0.6 < 0.83

∴ The fractions can be arranged in ascending order as follows: 2/5 < 1/2 < 3/5 < 5/6

Method 2

By converting the given unlike fractions into like fractions

Using the second method, we convert the denominators of all the given fractions into a common denominator by finding the LCM ( Least Common Multiple) of the denominators. Then, we multiply the same number by the numerator and denominator. After this step, we compare the values in the numerator of the fractions thus obtained and arrange them in increasing order. Let us use the same example to understand this.

Example: Arrange the following fractions in ascending order: 1/2, 2/5, 5/6, 3/5

Solution: We will convert the given unlike fractions into like fractions. The given fractions are 1/2, 2/5, 5/6, 3/5

LCM of {2, 5, 6} = 30

1/2 × 15/15 = 15/30

2/5 × 6/6 = 12/30

5/6 × 5/5 = 25/30

3/5 × 6/6 = 18/30

Now, that all the fractions are converted to like fractions, we can easily compare the numerators of these fractions, i.e., 12 < 15 < 18 < 25

⇒ 12/30 < 15/30 < 18/30 < 25/30

∴ The fractions can be arranged in ascending order as follows: 2/5 < 1/2 < 3/5 < 5/6

Decimals are numbers that have a whole number part and a fractional or decimal part connected through a decimal point. To arrange decimals in ascending order, first observe the whole number part. If it is greater than the other number, it means the number is greater than the other number. For example, 23.6 < 32.947 < 45.09. If two or more numbers have the same whole number part, for example, 2.45 and 2.09, then we look at the tenths place digit in the given numbers. Here, the tenths place digits are 4 and 0. Clearly 0 < 4, so 2.09 < 2.45. If the tenths place digits are also the same, then we observe the hundredths place digits, and so on. This is how we arrange decimals in ascending order.

Ascending order of negative numbers means arranging the given negative numbers from the smallest to the largest values. It is to be noted that in the case of negative numbers, the absolute values of smaller numbers are greater than the absolute values of larger numbers.

With negative numbers, the highest number with the negative sign has the least value.

Example: Arrange in ascending order: -34, -56, -4

Solution: The given integers can be arranged in ascending order as follows:

-56 < -34 < -4

-4 is the largest number and -56 is the smallest number out of the given three numbers. Observe the figure given below to understand ascending order and descending order of numbers on a number line.

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What is Ascending Order?

Ascending order in math is the arrangement to organize numbers/items from smallest to largest. It is one of the ways to organize items or numbers and is also known as increasing order. An example of numbers arranged in ascending order is 1 < 2 < 3 < 4.

What is Ascending Order and Descending Order?

Ascending order is the way to arrange numbers from lowest to highest values while descending order is the way of arranging numbers from highest to lowest values. They are opposite of each other.

How to Arrange the Numbers in Ascending Order?

Ascending order is an arrangement from the smallest to the largest value. For example, {4, 7, 10, 13} are numbers arranged in ascending order. While arranging numbers in ascending order, we write the smallest value first and then we move forward towards the larger values.

What is the Ascending Order Sign?

The symbol used to arrange numbers in ascending order is '<'. Therefore, the less than symbol or < is the ascending order sign. For example, when we arrange a given set of numbers in ascending order we express it as follows using the ascending order sign: 4 < 7 < 10 < 13

How to Arrange Fractions in Ascending Order?

Like fractions can be arranged in ascending order by arranging them as per the values of their numerators from smallest to largest values. While unlike fractions can be first converted to like fractions, and then we can arrange them in increasing order. For unlike fractions with the common numerator, the fraction with the largest number in the denominator has the smallest value, and the fraction with the smallest number in the denominator has the largest value. For example, 2/9 < 2/8 < 2/7 < 2/6 < 2/5.

What is the Difference Between Ascending and Descending Order?

When the numbers are arranged in the 'smallest to largest' pattern, they are said to be in ascending order. On the other hand, when the numbers are arranged in a 'largest to smallest' pattern, they are said to be in descending order.

How to Arrange Decimals in Ascending Order?

To arrange decimals in ascending order, we use the concept of comparing decimals. Decimals are arranged in ascending order by looking at the digits from left to right according to the place value of decimal numbers. First, we look at the whole number part. If the digit in the whole number part is the same for two or more numbers, then we look at the digit at the tenths place of the number (i.e., first digit to the right of the decimal point). If the digit in the tenths place is also the same, then we look at the digit at the hundredth place and so on. This is how we arrange decimals in ascending or increasing order. For example, 1.3 < 1.35 < 1.356 < 2.3 < 4.08.

How to Arrange Integers in Ascending Order?

Integers are numbers without the fractional or decimal part. They include whole numbers and their negatives on the other side of the number line. On a number line, if we move towards the right, then we get integers written in ascending order. For example, -5 < -4 < -3 < -2 < -1 < 0 < 1 < 2 < 3 < 4 < 5.