## What is Ascending Order?

Ascending order means to arrange numbers in increasing order, that is, from smallest to largest.

To arrange numbers in any order, we first need to compare them.

**Arranging numbers in ascending order:**

- Count the number of digits in each number. The number with the least number of digits is the smallest. Write it first. Continue this till all the numbers left for comparison have the same number of digits.
- For the numbers having the same number of digits, start with comparing the numbers from the leftmost digit. Write the number with the smallest digit.
- If the leftmost digits are same, move to the digits to the right and compare them. Write the number with smaller digit.
- Continue doing this with the remaining numbers till we arrange all the numbers.

**Example**: Arrange 22554, 231, 22, 245, 22354 in ascending order.

The number 22 has the least number of digits. So, write it first as it is the smallest number.

Next, 231 and 245 both are 3-digit numbers. They both have 2 at hundreds place. So, we move to the digit to the right. Compare 2**3**1 and 2**4**5 Since, 3 < 4; So, 231 < 245

Next, compare 22554 and 22354 as both have 5 digits. On comparing, 22**5**54 and 22**3**54, we find 3 < 5

So, 22354 < 22554

We can then also arrange the numbers on the number line as shown:

## Ordering Fractions in Ascending Order

**Ordering fractions with same denominators**

For the fractions having the same denominator, the fraction with the smallest numerator is the smallest.

** Example**: Arrange ^{3}⁄_{7 }, ^{2}⁄_{7 }, ^{5}⁄_{7 }, 1⁄_{7} in ascending order.

Comparing the numerators, we get 1 < 2 < 3 < 5

Therefore, 1⁄_{7} < ^{2}⁄_{7} < ^{3}⁄_{7} < ^{5}⁄_{7}

**Ordering fractions with same numerators**

When the fractions have the same numerator, the fraction with the highest denominator is the smallest.

** Example**: Arrange ^{3}⁄_{7 }, ^{3}⁄_{8 }, ^{3}⁄_{5 }, ^{3}⁄_{4} in ascending order.

Here, the numerator is 3 in all the fractions. So, we compare the denominator.

On comparing the denominators, we get: 4 < 5 < 7 < 8

Therefore, ^{3}⁄_{8 }< ^{3}⁄_{7 }< ^{3}⁄_{5} < ^{3}⁄_{4}

**Ordering fractions with different numerators and denominators**

Convert the fractions to the like denominators (or numerators) and then compare and order them.

** Example**: Arrange ^{2}⁄_{5}, ^{4}⁄_{6}, ^{3}⁄_{5} and ^{1}⁄_{3} in ascending order.

Here, the denominators are 5, 6 and 3.

LCM of 3, 5 and 6 is 30.

So, we find the equivalent fractions.

**Ordering Decimals in Ascending Order**

- First compare the whole number part in each decimal. The number with smallest whole number is the smallest.
- If the whole number parts are the same, compare the decimal parts just as we compare the whole numbers.

**Example**: Arrange 22.44, 22.04, 22.40, and 2.45 in ascending order.

First compare whole numbers:

22.44, 22.04, 22.40, and 2.45

2 is the smallest, we write it first.

2.45 |

22.44, 22.04, 22.40 all have 22.

So, compare the decimal parts.

0.04 < 0.40 < 0.44

Therefore, 22.04 < 22.40 < 22.44

The ascending order is:

2.45 | 22.04 | 22.40 | 22.44 |

Fun Facts– To remember ascending order, remember the flight of an “airplane”, from low to high. |

## Practice Problems

## Ascending Order## 1Arrange the following decimal numbers in ascending order - 4.3, 1.24, 2.4, 1.21.2 < 2.4 < 4.3 < 1.24 4.3 < 2.4 < 1.24 < 1.2 1.24 < 1.2 < 2.4 < 4.3 1.2 < 1.24 < 2.4 < 4.3 CorrectIncorrect Correct answer is: 1.2 < 1.24 < 2.4 < 4.3 Decimals are compared the same way as multi-digit numbers by keeping the number of digits the same with the help of trailing zeroes. ## 2Arrange the following fractions in ascending order - 3/7, 3/5, 3/9, 3/113/5 < 3/7 < 3/9 < 3/11 3/11 < 3/7 < 3/5 < 3/9 3/11 < 3/9 < 3/7 < 3/5 3/7 < 3/11 < 3/9 < 3/7 CorrectIncorrect Correct answer is: 3/11 < 3/9 < 3/7 < 3/5 For fractions with the same numerators, the fraction with the smallest denominator is the greatest fraction and the fraction with the greatest numerator is the smallest fraction. ## 3Arrange the following fractions in ascending order - 2/9, 3/9, 7/9, 5/92/9 < 3/9 < 5/9 < 7/9 7/9 < 5/9 < 3/9 < 2/9 2/9 < 7/9 < 5/9 < 3/9 7/9 < 5/9 < 2/9 < 3/9 CorrectIncorrect Correct answer is: 2/9 < 3/9 < 5/9 < 7/9 For fractions with the same denominators, the fraction with the smallest numerator is the smallest fraction and the fraction with the largest numerator is the greatest fraction. ## 4Arrange the following numbers in ascending order - 22, 2322, 2222, 22222 < 222 < 2322 < 2222 22 < 222 < 2222 < 2322 22 < 2222 < 222 < 2322 2322 < 2222 < 222 < 22 CorrectIncorrect Correct answer is: 22 < 222 < 2222 < 2322 While comparing multi-digit numbers, the numbers with the least number of digits come first. For multi-digit numbers with the same number of digits, we compare digits from left to right. |

## Frequently Asked Questions

**Is descending order smallest to largest?**

No. Descending order is from largest to smallest. The largest quantity or number is placed first and the smallest quantity or number is placed at the last position.

**Can we arrange fractions in ascending or descending order?**

Yes. Just like whole numbers, fractions can also be arranged in ascending or descending order.

**What symbols are used when arranging numbers in ascending and descending order?**

The symbols < (less than) and > (greater than) are used when arranging numbers in ascending and descending order. Ascending order: 3 < 5 < 15 < 21 Descending order: 21 > 15 > 5 > 3

**Do we look at the numerator or denominator when arranging fractions in ascending or descending order?**

If the numerators of a group of fractions are the same, we use the denominators to sort them in ascending or descending order. We look at the numerators if the denominators are the same. If the numerators and denominators are different, we compare the fraction sizes to sort them in ascending or descending order.