Ascending Order

Ascending order refers to the arrangement of numbers or other items in increasing order from smallest to largest. Numbers that we see on a number line from left to right is an example of ascending order. We usually represent it by putting commas between numbers or by using '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 Ascending 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, we try to arrange them in an increasing pattern. 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 minds. Those 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 '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 at the left is smaller in value than the number at 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:

• By converting fractions to decimals
• By converting given fractions into like fractions

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. And with the second method, we convert the denominators of all the given fractions into the LCM of the denominators by multiplying the same number to numerator and denominator. Then we compare the values in the numerator of the fractions so obtained and arrange them in increasing order.

For example, arrange the following fractions in ascending order: 1/2, 2/5, 5/6, 3/5. 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 have to look at the digit at the tenths place to arrange these numbers in ascending order.

0.4 < 0.5 < 0.6 < 0.83

∴ 2/5 < 1/2 < 3/5 < 5/6.

Now, let us look at the solution of the same example by using the like fractions method. 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, we can easily compare the numerators of these fractions, i.e 12 < 15 < 18 < 25.

⇒ 12/30 < 15/30 < 18/30 < 25/30

∴ 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, look at 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 look at the hundredths place digits, and so on. This is how we arrange decimals in ascending order.

Ascending order of negative numbers means to arrange the given negative numbers from smallest to largest values. It is very important to learn as in the case of negative numbers the absolute values of smaller numbers are greater than the absolute values of larger numbers, which makes it confusing.

With negative numbers, the highest number with the negative sign has the least value. So, if you have to arrange -34, -56, -4 into ascending order, then it is arranged in the following order:

-56 < -34 < -4

-4 is the largest number and -56 is the smallest number out of the given three numbers. Look at the image 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. It is also known as increasing order. An example of 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 arrangement from highest to lowest values. They are opposite of each other.

How do you Arrange Numbers in Ascending Order?

Ascending order is an arrangement from smallest to 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, less than symbol or < is the ascending order sign.

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 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 right, then we get integers written in ascending order. For example, -5 < -4 < -3 < -2 < -1 < 0 < 1 < 2 < 3 < 4 < 5.