# What are the largest and smallest 10-digit numbers?

The method to represent and work with numbers is known as the number system. A number system is a system of writing to represent numbers. It is the mathematical notation used to represent numbers of a given set by using digits or other symbols. It has arithmetic operations to perform division, multiplication, addition, and subtraction between numbers. Some important number systems are as follows,

- Decimal Number System
- Binary Number System
- Octal Number System
- Hexadecimal Number System

### Numbers and Digits

Numbers are the counts or measurements used in mathematics, numerals are used to define numbers. A numeral can be defined as a symbol used for counting, for instance, there are 55 books in the library, where 56 is the numeral which is a combination of digits 5 and 6. A digit is a single numeral, the combination of digits form numerals. In the decimal number system, there are 10 digits, they are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

### What are the largest and smallest 10-digit numbers?

**The Largest 10 digit number in the number system is 9,99,99,99,999.**

**Explanation:**

If +1 is added to the number (9,99,99,99,999) it becomes 11 digit number that is 10,00,00,00,000 (11 digit number). So 9,99,99,99,999 is the largest 10 digit number in the number system. Largest 10 digit number = 9,99,99,99,999

= 9,99,99,99,999 + 1

= 10,00,00,00,000 (Which is a 11 digit number)

So it is proved the 9,99,99,99,999 is the largest 10 digit number in the number system.

**Smallest 10 digit number in the number system is 1,000,000,000.**

**Explanation:**

The smallest 10 digit number in the number system is 1,000,000,000 because if we subtract -1 from the number it becomes 9 digit number which is 99,99,99,999 (9 digit number). So 1,000,000,000 is the smallest 10 digit number in the number system. Smallest 10 digit number in the number system = 1,000,000,000

= 1,000,000,000 – 1

= 99,99,99,999 (which is a 9 digit number)

Hence it is proved that 1,000,000,000 is the smallest 10 digit number in the number system.

Therefore**, **the Largest 10 digit number in the number system is **9,99,99,99,999** and the smallest 10 digit number in the number system is **1,000,000,000**.

### Conceptual Problems

**Question 1: What is the smallest 1 digit number?**

**Answer**:

Smallest 1 digit number in the number system is 0.

**Question 2: What is the largest 1 digit number?**

**Answer**:

Largest 1 digit number in the number system 9.

**Question 3: What is the smallest 3 digit number?**

**Answer**:

The smallest 3 digit number in the number system is 100.

ExplanationIf -1 is subtracted from the number it becomes 2 digit number that is 99 (a two-digit number). So 100 is the smallest 3 digit number in the number system.Smallest 3 digit number= 100

= 100 – 1

= 99 (Which is 2 digit number)

So it is proved the 100 is the smallest 3 digit number in the number system.

**Question 4: What is the largest 3 digit number?**

**Answer**:

Largest 3 digit number in the number system 999.

ExplanationIf +1 is added to the number (999) it becomes 4 digit number that is 1000 (Four-digit number). So 999 is the largest 3 digit number in the number system. Largest 3 digit number= 999= 999 + 1

= 1000 (Which is 4 digit number)

So it is proved the 999 is the largest 3 digit number in the number system.

**Question 5: What is the smallest 5 digit number?**

**Answer**:

The smallest 5 digit number in the number system is 10000.

ExplanationIf -1 is subtracted from the number it becomes 4 digit number that is 9999 (Four digit number). So 10000 is the smallest 5 digit number in the number system. Smallest 5 digit number= 10000= 10000 – 1

= 9999 ( Which is 4 digit number )

So it is proved the 10000 is the smallest 5 digit number in the number system.

**Question 6: What is the largest 5 digit number?**

**Answer**:

The largest 5 digit number in the number system is 99999.

ExplanationIf +1 is added to the number (99999) it becomes 5 digit number that is 100000 (Six-digit number). So 99999 is the largest 5 digit number in the number system. Largest 5 digit number= 99999= 99999 + 1

= 100000 (Which is 6 digit number)

So it is proved the 99999 is the largest 5 digit number in the number system.