Grade 9 Chemistry Unit 2: 2.1.7 Scientific Notation and Decimal Places | Exercise 2.7

Introduction

This tutorial focuses on understanding scientific notation and decimal places as covered in Grade 9 Chemistry, Unit 2. These concepts are essential for accurately expressing large and small numbers, a common occurrence in scientific measurements. This guide will break down exercises related to these topics to enhance your understanding and application.

Step 1: Understanding Scientific Notation

Scientific notation is a method of expressing numbers that are too large or small to be conveniently written in decimal form. It is formatted as:

[ a \times 10^n ]

Where:

• a is a number greater than or equal to 1 and less than 10.
• n is an integer that indicates the power of ten.

How to Convert to Scientific Notation

1. Identify the significant figures in the number.
2. Move the decimal point to create a number between 1 and 10.
3. Count how many places you moved the decimal.
   • If you moved it to the left, n is positive.
   • If you moved it to the right, n is negative.
4. Write the number in the format ( a \times 10^n ).

Example

Convert 4500 to scientific notation:

• Move the decimal point 3 places to the left: 4.5
• Since it’s moved left, n = 3.
• Therefore, 4500 = ( 4.5 \times 10^3 ).

Step 2: Working with Decimal Places

Decimal places refer to the number of digits to the right of the decimal point. Understanding how to manage decimal places is crucial for precision in scientific calculations.

Rounding Decimal Places

1. Identify the number of decimal places required.
2. Look at the digit immediately after the last required decimal place.
   • If it’s 5 or more, round up the last digit.
   • If it’s less than 5, keep the last digit the same.
3. Write the rounded number.

Example

Round 3.45678 to three decimal places:

• Look at the fourth decimal (7).
• Since 7 is greater than 5, round up the third decimal (6) to 7.
• Result: 3.457.

Step 3: Practicing with Exercises

To reinforce your understanding, practice with the following exercises:

1. Convert the following numbers to scientific notation:

   • 0.00052
   • 1200000
   • 0.034

2. Round the following numbers to two decimal places:

   • 5.678
   • 9.1234
   • 2.555

Conclusion

Understanding scientific notation and decimal places is vital in chemistry and other sciences. This tutorial provided a clear framework for converting numbers and managing precision through rounding. To further enhance your skills, practice the exercises provided and seek additional problems in your textbook or online resources.