Cara Menulis Bilangan Dalam Bentuk Baku

Introduction

This tutorial will guide you on how to write numbers in scientific notation, also known as "bentuk baku" in Indonesian. Understanding this concept is essential for students in middle school (kelas 7 and 9) and is applicable in various mathematical contexts, including working with large and small numbers.

Step 1: Understanding Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small in a compact form. It is written 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 how many places the decimal point moves.

Practical Tips

• For numbers larger than 10, n is positive.
• For numbers smaller than 1, n is negative.

Step 2: Converting Large Numbers to Scientific Notation

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

1. Identify the first non-zero digit in the number.
2. Place the decimal point after this digit.
3. Count how many places you moved the decimal to the left; this will be your exponent (n).
4. Write the number in the format ( a \times 10^n ).

Example

Convert 45,000 to scientific notation:

• First non-zero digit: 4
• Decimal point placement: 4.5
• Count of places moved: 4
• Result: ( 4.5 \times 10^4 )

Step 3: Converting Small Numbers to Scientific Notation

For small numbers, the process is similar but involves moving the decimal point to the right:

1. Identify the first non-zero digit.
2. Place the decimal point after this digit.
3. Count how many places you moved the decimal to the right; this will be a negative exponent.
4. Write the number in the format ( a \times 10^n ).

Example

Convert 0.00056 to scientific notation:

• First non-zero digit: 5
• Decimal point placement: 5.6
• Count of places moved: 4 (to the right)
• Result: ( 5.6 \times 10^{-4} )

Step 4: Working with Decimal Numbers

When working with decimal numbers, follow the same principles as above. Ensure that the coefficient (a) remains between 1 and 10.

Example

Convert 3.2 to scientific notation:

• First non-zero digit: 3
• Decimal point placement: 3.2
• Since it's already in the required format, it remains: ( 3.2 \times 10^0 )

Conclusion

Understanding how to write numbers in scientific notation is crucial for handling both large and small values effectively. Remember the key steps:

• Identify the first non-zero digit.
• Adjust the decimal point accordingly.
• Count the moves to determine the exponent.

As a next step, practice with various numbers to become comfortable with the conversion process. You can also explore applications of scientific notation in real-world scenarios, such as astronomy or chemistry, to reinforce your learning.