Ascending & Descending Order: Fractions, Decimals

Ascending, Descending Order: When you see a flight of stairs, what is the first thing that comes to mind? Is it not similar to how, if you start from the bottom and want to go up, you increase the number of each stair flight until you reach the top-most step and vice versa? Ascending order means arranging numbers in ascending order from least to largest. The descending order, on the other hand, is when we arrange numbers in ascending order from a higher value to a lower one. Students also learn these to arrange the numbers from bigger to smaller numbers and also from smaller to bigger numbers. It is important for students to learn basic concepts like these as they are not only used in academics but also in their day to day activities. Ascending Order and Descending Order are minor concepts but have a major role in the subject as a whole.

In this article, we will cover the learning of ascending and descending order meaning, decimals, fractions, solved examples and more. Continue reading.

Ascending and Descending Order

We will now discuss in detail ascending and descending order here.

Ascending Order

Before we start, take a look at the ascending order example given below.

So, what is ascending order? When we access a vast amount of data, it is not easy to put it in a particular order. Ordering helps us to sort and filter the data in an organised manner. When the data is arranged in the order of smallest to largest, it is called ascending order.

Thus, ascending order means a sorting method in which the sort starts from the lowest to the highest.

We usually represent ascending order by putting commas between numbers or by using the less-than symbol (<) between numbers. For example,

\(7, 8, 9, 10, 11, 12\) or \(7<8<9<10<11<12\).

Have you ever encountered a situation where you have so many vital folders/files/documents that may be useful to you, but you can not find the correct one? Well, we can solve such problems by arranging them in some particular pattern or order. Setting things in ascending order is one way to collect and represent data.

Descending Order

Now, again have a look at the picture given below. 

What is descending order? If the numbers are arranged from the largest to the smallest number, it is said to be in descending order. In simple words, descending order is defined as an arrangement from the highest to the lowest. 

To arrange the numbers in descending order, we start with the largest number and move toward the smaller numbers one by one.  For representing descending order, we use greater than sign \((>)\). For example, \(18>15>11>6>3>1\).

Ascending, Descending Order: Rules

To arrange the numbers in descending and ascending order, the candidates need to follow some rules and regulations. Therefore, the rules for descending and ascending order are mentioned separately. Let us take a look at them.

Rules for Ascending Order

The following rules should be followed while arranging a given set of numbers in ascending order:

1. First, count the digits of the numbers. A \(1\)-digit number is always smaller than a \(2\)-digit number.
2. If all the numbers have an equal number of digits, then the number whose first digit is greater will be higher.
3. If the numbers have an equal number of digits and the first digits are the same, then compare the last digits.
4. The values should be in the order from smallest to largest.
5. The first value will always be the smallest, and the last value is always the largest.

Rules of Descending Order

The following rules should be followed while arranging a given set of numbers in descending order:

1. Always pick the largest number first, and, thus, the first number will be the largest.
2. Zero is greater than any negative number.
3. Positive numbers are greater than any negative number and zero.
4. Two-digit numbers are always greater than a one-digit number.
5. If all the numbers have an equal number of digits, then the number whose first digit is greater will be higher.
6. If the numbers have an equal number of digits and the first digits are the same, then compare the last digits.

Ascending And Descending Order in Maths

In Mathematics, ascending order meaning the numbers which can be arranged from the smallest number to the largest number. It will be vice-versa if we are talking about the descending order. This order in Mathematics will help the students at the primary school to learn about the arrangement of numbers in the decreasing or increasing order to solve the problem. The arrangement of these numbers can be made in any of the real number systems.

Ascending and Descending Order of Negative Numbers

You can arrange in ascending order by placing the given negative numbers from smallest to largest values. We can arrange them from the largest value to the smallest if we need to settle them in descending order. This is because the absolute values (the magnitude of a real number without regard to its sign) of smaller numbers are greater than the absolute values (the magnitude of a real number without regard to its sign) of larger numbers. But, so many times, people find it confusing. And, thus it is easy to arrange the positive integers in ascending order, but we have to be careful with negative integers. The highest number with a minus sign (-) is of the smallest value. 

In negative numbers, the lowest number with the negative sign has the highest value. So, if you have to arrange \(-34, -56, -4\) into ascending and descending order, then it is arranged in the following order: 

\(-56 < -34 < -4\) and \(-4 > -34 >-56\) respectively.

Here, \(-4\) is the largest number, and \(-56\) is the smallest number out of the three numbers.

Ascending and Descending Order of Fractions

The ascending order of the fractions means arranging the given fractions in the increasing order, whereas descending order means setting the given fraction values in the decreasing order. While arranging the fraction values in ascending or descending order, the students need to follow the two ways to arrange them. Check the below-provided methods.

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

We can convert fractions to decimals by actually dividing the numerator with the denominator. Then we can do the arrangement of those decimals in ascending or descending order by looking at the whole number part and the decimal part place values.

For example: Arrange the given fractions \(3\frac{6}{{25}},2\frac{3}{5},3\frac{1}{{25}}\) in ascending order.

\(3\frac{6}{{25}} = \frac{{81}}{{25}} = 3.24\)

\(2\frac{3}{5} = \frac{{13}}{5} = 2.6\)

\(3\frac{1}{{25}} = \frac{{76}}{{25}} = 3.04\)

Arranging the given decimal numbers in descending order, we get,

\({\rm{3}}{\rm{.24 > 3}}{\rm{.04 > 2}}{\rm{.6}}\)

Thus, \(3\frac{1}{{25}} > 3\frac{6}{{25}} > 2\frac{3}{5}\)

For the second method, we should first find the LCM of the denominators of all the fractions. Then, convert the denominators of the given fractions into like fractions by finding the LCM of the denominators. Then compare the values in the numerator of the fractions obtained and arrange them in increasing or decreasing order.

For example, compare the fractions \(\frac{2}{3},\frac{3}{4} = \frac{5}{{12}} = \frac{9}{{16}}\) by writing them in ascending order

LCM of the denominators \(3, 4, 12\) and \(16 = 48\)

Therefore,

\(\frac{2}{3} = \frac{{2 \times 16}}{{3 \times 16}} = \frac{{32}}{{48}}\)

\(\frac{3}{4} = \frac{{3 \times 12}}{{4 \times 12}} = \frac{{36}}{{48}}\)

\(\frac{5}{{12}} = \frac{{5 \times 4}}{{12 \times 4}} = \frac{{20}}{{48}}\)

\(\frac{9}{{16}} = \frac{{9 \times 3}}{{16 \times 3}} = \frac{{27}}{{48}}\)

Now, see the numerator of these like fractions. The fraction with the largest numerator is the largest.

Thus, \(\frac{{20}}{{48}},\frac{{27}}{{48}},\frac{{32}}{{48}},\frac{{36}}{{48}}\) i.e. \(\frac{5}{{12}},\frac{9}{{16}},\frac{2}{3},\frac{3}{4}\)

Ascending and Descending Order in Decimal Numbers

Decimal numbers are arranged in ascending or descending order by looking at the place value of decimal numbers. Firstly check the whole part of the decimal number, in case, if the whole number digits are the same then look at the digit in tenth place. If the digit at tenths place is also the same, then check the digits at the hundredth place and so on.

For example, \(1.09> 2.07 > 2.40 > 2.45 > 3.7 > 4.8\) shows the arrangement of decimal numbers in ascending order. 

And, \(4.8 > 3.7 > 2.45 > 2.40 > 2.07 > 1.09\) shows the arrangement of decimal numbers in descending order.

Solved Examples On Ascending Order, Descending Order

Q.1. Arrange the following numbers in descending order.\(25, 67, 45, 87, 19, 91, 24, 44, 56\) and \(34\)
Ans: Arranging the numbers from largest to the lowest is known as descending order.
Thus, the numbers in descending order are \(91, 87, 67, 56, 45, 44, 34, 25, 24\) and \(19\).

Q.2. List the following dates in ascending order.\(17th\) July \(1995\), \(10th\) March \(1990\), \(29th\) February \(1984\), \(17th\) July \(1996\)
Ans: This is how you arrange in ascending order-
\(29th\) February \(1984\), \(10th\) March \(1990\), \(17th\) July \(1995\), \(17th\) July \(1996\).

Q.3. Arrange the decimal numbers in descending order.\(3.6, 3.69, 3.61, 5. 006, 5.069, 3.72, 3.70\) and \(3.00\)
Ans: Thi is how you arrange in descending order-
\(3.00, 3.6, 3.61, 3.69, 3.70, 3,72, 5.006\) and \(5.069\)

Q.4. Arrange the given amount of money in ascending order.\(₹100,₹101,₹99,₹75,₹200,₹98,₹55\)
Ans: Ascending order example for the arrangement of the given amount of money is as follows-
\(₹55,₹75,₹98,₹99,₹100,₹101,₹200\)

Q.5. Arrange the given following negative numbers in descending order. \(-1, -45, -23, -101, -32, -40\)
Ans: While arranging the negative numbers in descending order, the highest number with a minus sign (-) is the smallest value. Thus, the arrangement is as follows-
\(-1>-23 >-32 >-40 > -45 > -100\)

Summary

In this article, we learned about what ascending order means. We also delved into descending order. We also learned about the rules to follow while arranging the numbers in ascending order and descending order.  We applied those rules in finding the ascending and descending order of fractions, decimal numbers, and negative numbers.

FAQs

We have provided some frequently asked questions about ascending and descending order here:

Q.1. Is ascending order smallest to largest?
Ans: Yes, whenever we arrange the numbers from a lower value to a higher value, the arrangement is known as ascending order. In this arrangement, we place the smallest value first and move towards the larger number.

Q.2. How to arrange negative numbers in ascending order?
Ans: To arrange negative numbers, one should always remember that the highest number with a minus sign (-) or negative symbol is the smallest value.

Q.3. What is the difference between ascending and descending order?
Ans: When the numbers are arranged in the smallest to largest order, then they are said to be in ascending order, whereas when the numbers are arranged in largest to smallest order, then they are said to be in descending order.

Q.4. How do you explain descending order?
Ans: If the numbers are arranged from the largest to the smallest number, it is said to be in descending order. 

Q.5. How do you explain ascending order?
Ans: If the numbers are arranged from the smallest to the largest, it is said to be in ascending order. 

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