Bab 2 (II) Matematik Tingkatan 3 (kssm) : 2.2 Bentuk Piawai :Tukar nombor tunggal kpd bentuk piawai

Introduction

In this tutorial, we will explore the concept of scientific notation (bentuk piawai) as covered in the video by Cikgu Chong. This method is essential for expressing large or small numbers in a more manageable form. We will learn how to convert single numbers to scientific notation and vice versa.

Step 1: Understanding Scientific Notation

Scientific notation is a way to express numbers that are too large or too small in a concise format. It consists of two parts:

• A number between 1 and 10.
• A power of ten.

For example, the number 3000 can be expressed in scientific notation as:

• 3.0 × 10³

Key Points

• The first part (3.0) is the coefficient.
• The second part (10³) indicates how many places to move the decimal point.

Step 2: Converting Single Numbers to Scientific Notation

To convert a single number to scientific notation, follow these steps:

1. Identify the first non-zero digit in the number.
2. Move the decimal point to the right of that digit.

Count how many places you moved the decimal point to determine the exponent of 10

• If you moved to the left, the exponent is positive.
• If you moved to the right, the exponent is negative.

Example

Convert 45000 to scientific notation:

• Identify the first non-zero digit: 4.
• Move the decimal point to get 4.5.
• Count the moves: 4 (from 45000 to 4.5).
• Thus, 45000 = 4.5 × 10⁴.

Step 3: Converting Scientific Notation Back to Single Numbers

To convert from scientific notation to a single number, follow these steps:

1. Identify the coefficient and the power of ten.
2. Move the decimal point in the coefficient according to the exponent.
   • Move to the right for positive exponents.
   • Move to the left for negative exponents.

Example

Convert 6.2 × 10² back to a single number:

• Coefficient: 6.2
• Exponent: 2
• Move the decimal point 2 places to the right, resulting in 620.

Practical Tips

• Always ensure your coefficient is between 1 and 10 when writing in scientific notation.
• Check your work by converting back to the original number to ensure accuracy.

Common Pitfalls

• Forgetting to adjust the decimal point correctly can lead to incorrect results.
• Miscounting the number of places moved can change the value significantly.

Conclusion

Mastering the conversion between single numbers and scientific notation is a valuable skill in mathematics. By practicing these steps, you'll gain confidence in handling large and small numbers efficiently. As a next step, try converting a few more numbers on your own, both to and from scientific notation, to reinforce your understanding.