Ascending order-Definition, Solved Examples and FAQ

Arrangements of numbers from smaller to bigger are known as ascending order. In this article, we are going to understand the topics along with examples.

Ascending order 

Arrangement of numbers in an order such that we find larger values as we move forward is known as the ascending order of numbers.

Here the arrangement is from a smaller number to a larger number.

It is also known as increasing order. The first number is the lowest and the last number is the highest.

It is similar to climbing up the stairs. As we move forward, our height from the ground keeps on increasing.

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How to represent numbers in increasing order

The symbol “<” is used in-between numbers in ascending order.
The number on the right of the symbol “<” is always greater than the number on the left of this symbol.

Increasing Order for Negative numbers

The absolute value of a negative number is its value without the negative sign. For arranging negative numbers in ascending we have to refer to their absolute values.

The negative number having a greater absolute value is less than the negative number having a smaller absolute value. This implies greater the absolute value, the smaller is the negative number.

Examples: 

1. (- 2) < (- 1)

The absolute value of (-1) is 1 and the absolute value of (-2) is 2.

2 is greater than 1.

The greater is the absolute value, the smaller is the negative number.

Hence (-1) is greater than (-2).

 2. (- 6) < (- 5) < (- 4)

The absolute value of (-6) is 6, (-5) is 5 and (-4) is 4.

6 is greater than 5, which is greater than 4.

The greater is the absolute value, the smaller is the negative number.

Hence (-4) is greater than (-5), which is greater than (-6).

Increasing Order for fractions

Case-1:  When the denominator of the fractions are the same.

In a group of fractions having the same denominators, the fraction having the greater numerator is the greater one and vice-versa.

Example:

\frac{1}{7}, \frac{6}{7}, \frac{9}{7}

The given fractions have the same denominators.
Since 1 < 6 < 9, we can say that \frac{1}{7}<\frac{6}{7}<\frac{9}{7}.

Case-2: 

When the denominator of the fractions are different.

In a group of fractions having different denominators, we have to convert them into like fractions first and then arrange them in the increasing order of their numerators. 

Example:

\frac{1}{2}, \frac{2}{3}, \frac{1}{6}

The given fractions have different denominators. Hence we have to convert them into like fractions.

LCM of 2, 3 and 6 = 6

\frac{1}{2}=\frac{1 \times 3}{2 \times 3}=\frac{3}{6}

\frac{2}{3}=\frac{2 \times 2}{3 \times 2}=\frac{4}{6}

\frac{1}{6}=\frac{1 \times 1}{6 \times 1}=\frac{1}{6}

Since, 1 < 3 < 4, we can say that \frac{1}{6}<\frac{3}{6}<\frac{4}{6}.

Hence, \frac{1}{6}<\frac{1}{2}<\frac{2}{3}.

Increasing Order for decimals

A decimal number consists of two parts:

1. Whole number part (left side of the decimal point)
2. Decimal part (right side of the decimal point)

For arranging decimals in ascending order we have to follow the following steps:

1. First, arrange the decimal numbers in increasing order considering their whole number part only.

The greater is the whole number part, the greater is the decimal number.

2. If some numbers have the same whole part, we have to arrange them further considering their decimal part.

The greater is the decimal part, the greater is the decimal number when the whole number part is the same.

Examples:

• 2.3, 1.567, 1.98, 3.5, 4, 2.245

Step 1:

Arranging the numbers according to the increasing order of their whole number part.

1.567, 1.98, 2.3, 2.245, 3.5, 4

Step 2:

Comparing the decimal part of the numbers having the same whole number part.

In 1.567 and 1.98, the decimal part 567 is less than the decimal part 980. Hence 1.567 < 1.98.

In 2.3 and 2.245, the decimal part 300 is more than the decimal part 245. Hence 2.245 < 2.3.

Step 3:

Arranging the given numbers by the results obtained from step 1 and step 2:

1.567 < 1.98 <  2.245 < 2.3 < 3.5 < 4

Solved Examples

1. Arrange 1,5,3,9,2 and 10 in ascending order first and then in descending order also.

Solution: 

Ascending order

1 < 2 < 3 < 5 < 9 < 10

Descending order

10 > 9 > 5 > 3 > 2 > 1

2. Vickey, Mohit, Ashok and Rahul secured 80%, 98%, 95% and 85% respectively in the final exams. Arrange their marks in increasing order. Who scored the highest among all four boys? 

Solution: 

Marks of Vickey = 80%

Marks of Mohit = 98%

Marks of Ashok = 95%

Marks of Rahul = 85%

Arranging the marks in increasing order:
80% < 85% < 95% < 98%

Hence Mohit secured the highest marks and Vickey secured the lowest marks.

3. Priya, Sonia, Preeti and Neha have Rs 400, Rs 100, Rs 200 and Rs 300 respectively.

Solution:

Money with Priya = Rs 400

Money with Sonia = Rs 100

Money with Preeti = Rs 200

Money with Neha = Rs 300

Arranging the money in increasing order:

Rs 100 < Rs 200 < Rs 300 < Rs 400

Priya has more money than the other 3 girls.