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**Class 9 Maths Worksheet Chapter 1:** A number system serves as a method for naming or representing numerical values. These values are essential for counting and performing mathematical operations. There are different types of number systems, like decimal, octal, binary, and hexadecimal. In this article, we’ll learn about number systems in math, the different types, and how to convert between them with examples. If you’re in grade 12, this will be helpful for your math studies.

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## What are Number Systems?

A **number system** is a way of writing numbers using digits or symbols consistently. It helps represent numbers uniquely and perform math operations like addition, subtraction, multiplication, and division. To understand a number in a system, you need to know the digit, its position in the number, and the base of the system.

Now, what’s a number? Well, it’s just a way to count or measure things. We use numbers every day, like when we count money or tell time. They’re important for understanding quantities and doing calculations.

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## What is a Number?

A number is a math thing we use for counting, measuring, or naming stuff. We use numbers for doing math like adding, subtracting, and so on. Examples of numbers include ones we count with, like 1, 2, 3, and so on. There are also special kinds of numbers like 0, which means nothing, and others like fractions and decimals.

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Numbers can be different in many ways. Some are even, like 2, 4, 6, because they can be divided by 2 evenly. Others are odd, like 3, 5, 7, because they can’t be divided by 2 evenly. There are also prime numbers, like 2, 3, 5, which can only be divided by themselves and 1. And there are composite numbers, like 4, 6, 8, which can be divided by other numbers too.

In our number system, we use digits to show numbers. Like in the number 10, we have the digits 1 and 0. We often use 0 and 1 for binary numbers, which are used in computers. But for regular counting, we use the digits from 0 to 9.

## Number System Class 9 Worksheet PDF

The number system is how we write and work with numbers. It helps us express numbers using digits or symbols. It’s important for math because it lets us do calculations like adding, subtracting, and dividing. Each number has its own value, which depends on its digit, position, and base. Numbers are used to count or measure things.

In Class 9, students learn about the number system. They study different types of numbers and how to solve equations involving them. Worksheets like the Number System Class 9 worksheet and the operations on Real Numbers Class 9 worksheet help students understand and practice these concepts. You can click on the link to download the Number System Class 9 Worksheet pdf.

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## Class 9 Maths Worksheet Chapter 1 Number System – Important Questions

The following important Number system questions for 9th grade students will help them become acquainted with a wide range of questions and thus develop problem-solving skills.

**Question 1: Find five rational numbers between 1 and 2.**

To find rational numbers between 1 and 2, we can use fractions. Let’s use a common denominator of 6.

**Answer:**

7/6

8/6

9/6

10/6

11/6

**Question 2: Find five rational numbers between 3/5 and 4/5.**

We’ll use a similar approach as before.

**Answer:**

19/30

20/30

21/30

22/30

23/30

**Question 3: Locate √3 on the number line.**

**Answer:** Draw a right-angled triangle where one side is 1 and the other side is √3. Then, measure the distance on the number line.

**Question 4: Are the square roots of all positive integers irrational? Provide an example.**

**Answer: **No, some square roots of positive integers are rational. For example, the square root of 16 is 4, which is rational.

**Question 5: Find the decimal expansions of 10/3, 7/8, and 1/7.**

**Answer:**

10/3 = 3.333…

7/8 = 0.875

1/7 = 0.1428571…

**Question 6: Explain how to convert a repeating decimal like 0.333… to a fraction.**

**Answer: **We can represent 0.333… as 1/3. We do this by letting x = 0.333… and solving the equation 10x = 3.

**Question 7: Determine the maximum number of digits in the repeating block of digits in the decimal expansion of 1/17.**

**Answer:** The maximum number of digits in the repeating block of 1/17 is 16.

**Question 8: Find three different irrational numbers between 5/7 and 9/11.**

**Answer: **Some examples of irrational numbers between 5/7 and 9/11 are 0.720720072…, 0.730730073…, and 0.808008000…

**Question 9: Visualize 3.765 on the number line using successive magnification.**

**Answer:** Use a ruler and magnify each part of the number line successively to locate 3.765.

**Question 10: Add 2√2 + 5√3 and √2 – 3√3.**

**Answer: **Simplify the expression to get 3√2 + 2√3.

**Question 11: Simplify (√3+√7) (√3-√7).**

**Answer:** Use the difference of squares formula to simplify to -4.

**Question 12: Rationalize the denominator of 1/[7+3√3].**

**Answer: **Rationalize the denominator to get (7 – 3√3)/22.

**Question 13: Represent √(9.3) on the number line.**

**Answer: **Locate √(9.3) on the number line by measuring its distance from the origin.

**Question 14: Simplify (i) 72/3.71/5 (ii) 101/2/101/4.**

**Answer:**

(i) Simplify to 713/15.

(ii) Simplify to 101/4.

**Question 15: What is the product of a rational and an irrational number?**

**Answer: **The product of a rational and an irrational number is always irrational.

**Question 16: What is the value of (256)0.16 X (256)0.09?**

**Answer:** The value is 4.

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## Types of Number Systems

In math, there are different number systems we use. The main ones are:

**Decimal:**This is our everyday number system, based on 10.**Binary:**It’s a system based on 2, using only 0s and 1s.**Octal:**This system is based on 8.**Hexadecimal:**It’s based on 16 and uses numbers 0-9 and letters A-F.

### Decimal Number System:

The number system we use every day is called the decimal system. It’s based on ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. When we write numbers without specifying a base, it’s assumed to be in the decimal system. For instance, numbers like 723, 32, and 4257 are all in the decimal system.

### Binary Number System:

The binary number system uses only two digits: 0 and 1. Each digit is called a bit. Eight bits together make a byte. Computers store data using bits and bytes. Binary numbers have a base of 2. They don’t use numbers like 2, 3, 4, or 5. Examples of binary numbers include 10001, 11110, and 1010101.

### Octal Number System:

The octal number system has 8 digits: 0, 1, 2, 3, 4, 5, 6, and 7. It’s based on groups of 8. Unlike some other systems, it doesn’t use digits like 8 or 9. This makes calculations simpler and reduces errors. It’s similar to binary but uses digits from 0 to 7. Octal numbers are commonly used in minicomputers. For instance, 358, 238, and 1418 are examples of octal number.

### Hexadecimal Number System:

The hexadecimal number system has 16 digits, including numbers 0 to 9 and letters A to F, representing values from 10 to 15 in decimal. It’s used in computers to simplify long binary strings. For instance, numbers like 7B3, 6F, and 4B2A are in hexadecimal format.

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## Class 9 Maths Worksheet Chapter 1 FAQs

### What is a number system?

A number system is a way of writing numbers using digits or symbols consistently. It helps us represent numbers and do math easily.

### What are the main types of number systems?

The main types of number systems are decimal, binary, octal, and hexadecimal.

### What is the decimal number system?

Decimal is our everyday number system based on ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

### What is the binary number system?

Binary uses only two digits, 0 and 1. It's the language computers understand, using bits and bytes.

### What is the octal number system?

Octal uses digits from 0 to 7 and is based on groups of 8. It's simpler for some calculations and is used in minicomputers.