Larger numbers are those kinds of numbers that have more digits or have longer figures. Therefore, they represent greater quantities when compared to usual smaller numbers, like numbers with 5 to 10 digits. 

When the number system is considered, each digit’s place is considered to have its own value, starting from the unit's place. 

Elaborately put, the places are units (1), tens (10), hundreds (100), thousands (1,000), ten thousands (10,000), lakhs (1,00000), and crores (10 000 000). These numbers are read differently after 10,000 in the international system. 

Importantly, in a number, as we move toward the left, each place is found to have ten times greater than what is there on the right. 

For example, let us consider the number 34,56,789 (in words: thirty-four lakh fifty-six thousand seven hundred eighty nine). In such a case, the digit 3 is read as 30 00 000 (three crores), the 4 indicates 4 00 000 (four lakhs), and so on.

Table of Contents:

• Why Do We Need Larger Numbers in Real Life--What is the Need?
• Solved Examples in Real Life Context
  1.    Counting Book Pages in a Digital Library
  2.    Population of a Small Town
  3.    Tracking a Fundraising Goal
•  Practice Numerical Problems
  1.    Counting Mangoes in a Warehouse
  2.    Calculating Distance to a Friend’s Village
  3.    Counting Stars in a Telescope Image
  4.    Inventory of School Chairs
  5.    Tracking Steps on a Fitness App

Why Do We Need Larger Numbers in Real Life--What is the Need?

Let us think of a situation of a school library with many, many books-- say, 12345 books. Similarly, consider the situation of measuring the population (number of people) of a city, like 2345678 people. 

In both scenarios, we can’t just go about measuring the numbers in hundreds or thousands, Precisely, we require a larger number system that describes the numbers that is easy to understand. 

In other words, the system should be such that it becomes comfortable to count how many objects there are and visualize.

This is where the use of larger numbers comes into play and makes the work easy. 

In fact, the use of larger numbers can aid in scenarios related to national budgets. These budgets go into huge numbers (often crores or even thousands of crores of rupees), 

With larger numbers, it also becomes easy to calculate and remember the distance away from a galaxy or stars--billions of kilometers. The distances can also be between planets in our own solar system--millions of kilometers.

This can also be useful in astronomy again for understanding the stars in different galaxies (hundreds of billions!). 

Thus, without the system of larger numbers, it would become extremely tough to keep track of big quantities. 

This can vary from counting money, understanding the total number of plants, or noting the total population of a country. When it comes to the storage of data, it becomes an indispensable aspect.

Solved Examples in Real Life Context

Counting Book Pages in a Digital Library
Suppose an online library contains many books (123,456) e-books. But to understand how many ten thousands are there, we need to know the number place. 

As per the international system, number 1 is at the millions place.
That is, we note the number '2' is in the ten thousands place (20,000). The number '3’ in the thousands place (3,000), etc. 

So, in total, 123,456 means one hundred twenty-three thousand four hundred fifty-six e-books in the international system.

In the Indian system, 1,23,456: One lakh twenty-three thousand four hundred and fifty-six.

Population of a Small Town
It was found that the town of Greenvale had a population of 45,678 people. Here, ‘4’ is in the ten thousands place (40,000), '5' in the thousands (5,000), '6' in the hundreds (600), and so on. Greenvale’s total population adds up exactly to forty-five thousand six hundred seventy-eight.

Tracking a Fundraising Goal
A charity organization aims to collect an amount of 2,500,000 dollars for new playgrounds and other charity expenditures. 

Going by the International system, the '2' in the millions place stands for two million. Next, the '5' in the hundred thousands place stands for five hundred thousand. Together, there is two million five hundred thousand dollars.

In the Indian system, 25,00000 dollars, it is twenty-five lakh dollars.

Practice Numerical Problems

1. Counting Mangoes in a Warehouse
Question: There is a fruit warehouse, and it can store 92,842 mangoes within it.  How many ten thousands are there in 92,842, and what are the remaining mangoes?
Answer & Explanation: The digit ‘9’ is in the number 92,842 in the ten thousands place—10,000. The number 2 is in the thousands place and 8 in the hundreds place. So, there are 9 ten thousands (i.e., 90,000), plus the remaining 2,842 mangoes.

2. Calculating Distance to a Friend’s Village
Question: The road sign on the side of the highway shows 3215 meters to reach the village of Raj. Determine what will be the value of the digit ‘2’ in 3215 and the total distance?
Answer & Explanation: The ‘2’ in our case is in the hundreds place when the number 3215 is considered. Hence, it represents 200 meters; therefore, Raj’s village is three thousand two hundred fifteen meters away.

3. Counting Stars in a Telescope Image
Question: A telescope detected many stars, and the picture showed 12345 stars. How many thousands and hundreds are in the number 12345?
Answer & Explanation: ‘12345’ means we need to use a comma to read the number. So the number is 12,345, which means it has 12 thousand (12000) stars to begin with. Then add three hundred (300) and forty-five stars to it. In total, we would see twelve thousand three hundred forty‑five stars.

4. Inventory of School Chairs
Question: A school arranges an annual party for students, and it orders 1234 chairs. Look at the number and determine which place‑value does the number ‘1’ stand for in 1234? Also, write down the remaining chairs and the total number of chairs in words.
Answer & Explanation: When written with a comma, the number can be rewritten as 1,234. Thus, number ‘1’ sits in the thousands place, which means that 1000 chairs are there. Next, we need to add the remaining 234 chairs, which gives out a total of one thousand two hundred thirty‑four.

5. Tracking Steps on a Fitness App
Question: Yesterday, Lina managed to walk many steps--9146 steps precisely. Now, check out the number and determine the value of the ‘1’ in 9146?
Answer & Explanation: The number ‘1’ in 9146 is clearly in the hundreds place, and thus, it amounts to 100 steps. Thus, Lina walked nine thousand one hundred forty-six steps in all.