Comparing Numbers--Different Types: Larger and Smaller Numbers (Class 6 Maths)
In real life, it becomes necessary to compare quantities, especially while dealing with some materials or the number of people. The best examples can be comparing packages that have to be delivered.
Another example can be the number of people residing in two different cities or the cost of different items.
It can also be related to the population in different parts of the globe--say, India, China, the US. Obviously, in all these cases, the numbers are going to be different, and hence we may have to understand them.
From a student's angle, it can be comparing the cost of two pencils. That is: one can be ₹12 and another can be ₹10--comparing prices here.
Thus, in this case, by comparing the numbers, we can figure out which pencil is costlier. This will be based on the number of digits in each number--greater or smaller. Hence, in many ways, comparing numbers helps to understand the differences in cost or the number of materials present.
In other words, comparison of numbers is an essential part of our lives. In fact, without its understanding, it will be difficult for us to purchase things.
In fact, it is due to the comparison of numbers that we can lay down the benchmark for any measurement.
Table Of Contents:
- Comparing Numbers--Different Types: Larger and Smaller Numbers
- Definition and Explanation
- Comparing Numbers: Numerical Problems with Answers
- Arranging the ascending and descending order of different numbers by counting Digits
- Definition of Ascending and Descending Order of Different Numbers
- Numerals Based on Largest/Smallest and Ascending/Descending Order
- Word Problems With Answers Based on the Largest and the Smallest Numbers
- School and Library Books Count
- Counting the Number of Shells—Largest and Smallest
- Counting Mangoes and Bananas—Largest and Smallest
Definition and Explanation
When different numbers are compared with each other, we find out which number is greater. Obviously, the number with the many number (greatest) of digits is always referred to as the largest (biggest) one.
In the same lines, the number with the fewest number (less, minimal) of digits in a set of numbers is referred to as the smallest.
Example: Let’s compare the numbers of different denominations: 45, 897, 5678, 9.
Here, it is clear that the number 45, having 2 digits, is the third greatest when it is compared to others.
In this case, it is obvious that the number 897 (having 3 digits) can be regarded as the second greatest.
In this case, it can be noted that the number 5678 has 4 digits--the largest of all.
Of all, the number 9 has only 1 digit--the smallest of all.
Thus, it can be understood that, by comparing digits, 5678 is the largest among all of the numbers.
On the other hand, when compared to other numbers, 9 turns out to be the smallest number. The reason for 5678 to be the largest is that it has four digits, while the number nine has only one digit.
This rule works owing to the use of the number system. That is, each place value (like ones, tens, hundreds, thousands) increases the value of the number ten times!
Comparing Numbers: Numerical Problems with Answers
Q1: There are two digits given: 876 or 87 (check digits). You have to compare them and write down which number is bigger.
Answer: It can be noticed that the number 876 has three digits, while 87 has two digits.
So, 876 is bigger because more digits mean a bigger number.
Q2: From the given set of numbers: 32, 5, 276, 9800, pick the smallest number.
Answer: To solve this question, let us start counting the number of digits in each number.
We noticed that in the number 32, there are two digits. In the number 5, there is one digit, while in the number 276, there are three digits.
However, in the number 9800, we notice that there are four digits. Thus, by comparing all these numbers, we notice that 9800 is the largest, while five is the smallest among all.
The number with the less digits is clearly 5 (1 being its only digit), so it turns out to be the smallest among all.
Q3: You have been given two numbers, and they are 19000 or 999. So, make a comparison and find out the digits in both. From this comparison, make a comment on which one is the largest (biggest) and which one is the smallest (lesser digits).
Answer: We can clearly note that the number 19,000 has five digits. When we consider the number 999, we notice that it has three digits.
When we make the comparison between the two numbers, it is obvious that 999 is the smallest. The reason behind it is that it has less number of digits when compared to the number 19,000.
So, we come to the conclusion that 19,000, which has five digits, is greater than 999, which has three digits.
Arranging the ascending and descending order of different numbers by counting Digits
Definition of Ascending and Descending Order of Different Numbers
When we say ascending order, it means that we place numbers from smallest to largest.
For descending order (lessening) of numbers, place the numbers starting from the largest (biggest one) to the smallest (least number).
Numerals Based on Largest/Smallest and Ascending/Descending Order
You have been given different numbers with different digits. You'll have to arrange them such that they appear in ascending order: 1, 210, 34, 56789. Then, you can rearrange them so that they can be put in descending order.
Answer: To start with, we have to count the number of digits in the given numbers (take each into consideration). They are as follows: we start with the lowest one.
1 → 1 digit
34 → 2 digits
210 → 3 digits
56789 → 5 digits
Answer: Ascending: 1, 34, 210, and 56789; descending: 56789, 210, 34, and 1.
Q5: Find the largest number and put them in ascending and descending order. Numbers are: 679, 46, 8, 70000.
Answer: Again, we have to start by counting the digits in each number.
8 → 1 digit
46 → 2 digits
679 → 3 digits
70,000 → 5 digits
So, the number with the most digits (many of all) is 70,000--the largest one.
Ascending order: 8, 46, 679, and 70,000.
Descending order: 70,000, 679, 46, and 8.
Word Problems With Answers Based on the Largest and the Smallest Numbers
School and Library Books Count
Q1: A school in a village was found to have 4200 students, while a city library has 45000 books. Check the digits and comment on which has the greater number?
Answer: Let’s check how many digits each number has:
The number: 4,200 → 4 digits
The number: 45,000 → 5 digits
Comparing the two numbers as per their digits, it is easy to come to a conclusion. Since 45,000 has more digits, the library has a greater number of books than the school has students.
Counting the Number of Shells—Largest and Smallest
Q2: Ria collected 15 shells on the beach, while her brother collected 1450. Based on the digits of each number, figure out who collected more?
Answer:
The number: 15 → 2 digits
The number: 1450 → 4 digits
So, Ria’s brother collected more shells, because the number 1450 has more digits than 15.
Counting Mangoes and Bananas—Largest and Smallest
Q3: A farmer grows 850 mangoes and 695 bananas. Check out the digits/largest number while checking mangoes and bananas. Then comment, find out which fruit does he grow more?
Answer:
The number: Mangoes: 850 → 3 digits
The number: Bananas: 695 → 3 digits
In this case, we noticed that the number of digits in bananas as well as mangoes is are same. But the number of mangoes is more than bananas. That is, the number 850 is greater than 695. Hence, we come to the conclusion that the farmer grew more mangoes than bananas.
