Exercise 2.1 Class 9 Math [2025]
This Exercise 2.1 Class 9 Math is start of unit 2: Logarithms. In this article, you’ll find the complete and easy-to-understand solutions for Exercise 2.1 Class 9 Math. This exercise introduces students to scientific notation, standard form, and how to handle very large or very small numbers efficiently. We’ve designed this post to guide you through important definitions, formulas, and key ideas, along with examples and video support to make learning easier. These notes are especially helpful for government school students who need clear and simple explanations in one place.
Download/ View PDF Notes
Key Concepts of This Exercise
This exercise 2.1 Class 9 math helps students understand how to work with very large and very small numbers in a simplified way. The main concepts are:
- Scientific Notation: A method used to express numbers that are too large or too small to be conveniently written in decimal form. It simplifies calculations and helps in representing measurements more efficiently in science and engineering.
- Standard or Ordinary Form: This is the regular way we write numbers in daily life using decimal points. Scientific notation can be converted into standard form to make it easier for general understanding.
- Powers of 10: Scientific notation works using powers of 10. Each power of 10 tells us how many places to move the decimal point to the right or left. A positive power indicates a large number; a negative power indicates a small number.
- Conversion Between Forms: The exercise teaches how to convert a decimal number into scientific notation and vice versa. Students learn to shift the decimal point and adjust the exponent accordingly.
- Use of Exponents: Understanding and applying exponent rules is important when expressing or simplifying numbers in scientific notation.
Definitions to Remember
Scientific Notation:
A number written in the form a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.
Example:
4,900 = 4.9 × 10³
0.00042 = 4.2 × 10⁻⁴
Standard Form (Ordinary Notation):
A way of writing numbers without using exponents.
Example:
3.2 × 10⁴ = 32,000
1.5 × 10⁻³ = 0.0015
Exponent:
The number of times the base (usually 10 in scientific notation) is multiplied by itself.
Example:
10³ = 10 × 10 × 10 = 1,000
Base 10:
A number system based on powers of 10. In scientific notation, the base is always 10.
Example:
2.7 × 10² has base 10 and exponent 2, meaning
2.7 × 100 = 270
Example Problems
Common Mistakes and How to Avoid Them
1. Incorrect Placement of the Decimal Point
One of the most common errors is moving the decimal point the wrong number of places or in the wrong direction when converting a number into scientific notation.
Example (Mistake):
Writing 45,000 as 4.5 × 10³ is wrong because the decimal was moved only 3 places.
Correct:
45,000 = 4.5 × 10⁴
Tip:
Count how many places the decimal moves from its original position to just after the first non-zero digit.
2. Confusing Positive and Negative Exponents
Students often mix up when to use a positive or negative exponent, especially when dealing with small decimal numbers.
Rule:
- Positive exponent → large number (decimal moved left)
- Negative exponent → small number (decimal moved right)
Example (Mistake):
Writing 0.0025 as 2.5 × 10³ is incorrect.
Correct:
0.0025 = 2.5 × 10⁻³
Tip:
If the number is less than 1, the exponent should be negative.
3. Forgetting to Express Only One Non-Zero Digit Before the Decimal
In scientific notation, the number before the ×10ⁿ must always be between 1 and 10 (i.e., only one non-zero digit before the decimal point).
Example (Mistake):
Writing 53,000 as 53 × 10³ is not correct.
Correct:
53,000 = 5.3 × 10⁴
Tip:
Make sure your number looks like a × 10ⁿ, where 1 ≤ a < 10
Short Answer Questions
Q1: What is scientific notation used for?
A: Scientific notation is used to write very big or very small numbers in a short and easy form. It is helpful in science, math, and technology.
Q2: How do we write 1 million in scientific form?
A:
1 million = 1,000,000
In scientific notation: 1 × 10⁶
Q3: Why do we use powers of 10 in science and math?
A: Powers of 10 make it easy to write and work with large and small numbers. They also make multiplication and division faster.
Q4: What is the standard form of 3.5 × 10³?
A:
3.5 × 10³ = 3500
Q5: Convert 0.00057 into scientific notation.
A:
0.00057 = 5.7 × 10⁻⁴
Q6: In scientific notation, what does the exponent tell us?
A: The exponent tells us how many places to move the decimal point. A positive exponent moves the decimal to the right; a negative exponent moves it to the left.
Q7: What does 10⁰ equal?
A:
10⁰ = 1
(Any number raised to the power of 0 is always 1)
Q8: Which is bigger: 6.5 × 10³ or 5.1 × 10⁴?
A:
5.1 × 10⁴ is bigger because 10⁴ is greater than 10³.
Real Life Usage / Implications
1. Used in Astronomy to Measure Large Distances
In space science, distances between planets, stars, and galaxies are extremely large. Writing such huge numbers in normal form is difficult and confusing. That’s why scientists use scientific notation.
Example:
The speed of light is about 300,000,000 m/s, which is written as 3 × 10⁸ m/s in scientific notation.
The distance between Earth and the Sun is about 149,600,000 km, written as 1.496 × 10⁸ km.
2. Used in Biology and Chemistry to Represent Tiny Quantities
Biologists and chemists often deal with very small things like cells, bacteria, and atoms. These measurements are so small that writing them in standard form would be full of zeros. Scientific notation makes them simpler.
Example:
The size of a human red blood cell is about 0.0000075 m, which is 7.5 × 10⁻⁶ m in scientific notation.
The mass of a water molecule is around 0.00000000000000000000003 g, written as 3 × 10⁻²³ g.
3. Helpful in Computer Science and Physics
In physics, scientific notation is used to handle very fast speeds, very large forces, or very small particles. In computer science, it’s useful when working with data size, processing speed, or tiny time intervals.
Example (Physics):
The charge of an electron is 0.00000000000000000016 C, or 1.6 × 10⁻¹⁹ C.
Example (Computer Science):
A nanosecond is 0.000000001 seconds, which is 1 × 10⁻⁹ s.
Video Lecture
Dear students we hope that this comprehensive coverage of exercise 2.1 class 9 math will help you understand and master the concepts of scientific notation and common notation. If you missed out on the notes of unit 1: Real Numbers you can access them below.