B) Work Out \left(3.6 \times 10^{-5}\right) \div \left(1.8 \times 10^2\right ]. Give Your Answer In Standard Form.

by ADMIN 115 views

Introduction

In this article, we will delve into the world of mathematics and explore the concept of division with numbers in scientific notation. We will work out the expression (3.6×10−5)÷(1.8×102)\left(3.6 \times 10^{-5}\right) \div \left(1.8 \times 10^2\right) and provide the answer in standard form.

Understanding Scientific Notation

Before we begin, let's take a moment to understand what scientific notation is. Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It consists of a number between 1 and 10 multiplied by a power of 10. For example, the number 456,000 can be expressed in scientific notation as 4.56×1054.56 \times 10^5.

Step 1: Divide the Coefficients

To divide two numbers in scientific notation, we first divide the coefficients (the numbers in front of the powers of 10). In this case, we have:

3.61.8\frac{3.6}{1.8}

To divide these numbers, we can use long division or simply divide them as fractions:

3.61.8=2\frac{3.6}{1.8} = 2

Step 2: Subtract the Exponents

Next, we subtract the exponents of the powers of 10. In this case, we have:

10−5÷10210^{-5} \div 10^2

To subtract the exponents, we can use the rule that am÷an=am−na^m \div a^n = a^{m-n}. In this case, we have:

10−5÷102=10−5−2=10−710^{-5} \div 10^2 = 10^{-5-2} = 10^{-7}

Step 3: Combine the Results

Now that we have divided the coefficients and subtracted the exponents, we can combine the results to get the final answer:

(3.6×10−5)÷(1.8×102)=2×10−7\left(3.6 \times 10^{-5}\right) \div \left(1.8 \times 10^2\right) = 2 \times 10^{-7}

Conclusion

In this article, we worked out the expression (3.6×10−5)÷(1.8×102)\left(3.6 \times 10^{-5}\right) \div \left(1.8 \times 10^2\right) and provided the answer in standard form. We used the rules of scientific notation to divide the coefficients and subtract the exponents, and then combined the results to get the final answer.

Why is Scientific Notation Important?

Scientific notation is an important concept in mathematics because it allows us to express very large or very small numbers in a more manageable form. This is particularly useful in fields such as physics, chemistry, and engineering, where large or small numbers are often encountered.

Real-World Applications of Scientific Notation

Scientific notation has many real-world applications. For example, it is used to express the size of atoms and molecules, the distance between stars and galaxies, and the speed of light. It is also used in finance to express large or small amounts of money, and in medicine to express the concentration of chemicals in the body.

Common Mistakes to Avoid

When working with scientific notation, there are several common mistakes to avoid. These include:

  • Not following the rules of scientific notation: Scientific notation has its own set of rules, and it is essential to follow them to avoid errors.
  • Not using the correct exponent: When subtracting exponents, it is essential to use the correct exponent.
  • Not combining the results correctly: When combining the results of dividing the coefficients and subtracting the exponents, it is essential to get the final answer correct.

Conclusion

Introduction

In our previous article, we worked out the expression (3.6×10−5)÷(1.8×102)\left(3.6 \times 10^{-5}\right) \div \left(1.8 \times 10^2\right) and provided the answer in standard form. In this article, we will answer some frequently asked questions about scientific notation and division.

Q: What is scientific notation?

A: Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It consists of a number between 1 and 10 multiplied by a power of 10. For example, the number 456,000 can be expressed in scientific notation as 4.56×1054.56 \times 10^5.

Q: How do I divide numbers in scientific notation?

A: To divide two numbers in scientific notation, you first divide the coefficients (the numbers in front of the powers of 10) and then subtract the exponents of the powers of 10. For example, to divide (3.6×10−5)\left(3.6 \times 10^{-5}\right) by (1.8×102)\left(1.8 \times 10^2\right), you would first divide the coefficients: 3.61.8=2\frac{3.6}{1.8} = 2. Then, you would subtract the exponents: 10−5÷102=10−5−2=10−710^{-5} \div 10^2 = 10^{-5-2} = 10^{-7}.

Q: What is the rule for subtracting exponents?

A: The rule for subtracting exponents is that am÷an=am−na^m \div a^n = a^{m-n}. This means that when you divide two numbers with the same base (in this case, 10), you subtract the exponents.

Q: Can I use scientific notation to express very large numbers?

A: Yes, you can use scientific notation to express very large numbers. For example, the number 456,000 can be expressed in scientific notation as 4.56×1054.56 \times 10^5. This makes it easier to work with and understand the size of the number.

Q: Can I use scientific notation to express very small numbers?

A: Yes, you can use scientific notation to express very small numbers. For example, the number 0.000456 can be expressed in scientific notation as 4.56×10−44.56 \times 10^{-4}. This makes it easier to work with and understand the size of the number.

Q: How do I convert a number from standard form to scientific notation?

A: To convert a number from standard form to scientific notation, you need to move the decimal point to the left or right until you have a number between 1 and 10. Then, you multiply the number by a power of 10 that is equal to the number of places you moved the decimal point. For example, to convert the number 456,000 to scientific notation, you would move the decimal point 5 places to the left to get 4.56. Then, you would multiply 4.56 by 10510^5 to get 4.56×1054.56 \times 10^5.

Q: How do I convert a number from scientific notation to standard form?

A: To convert a number from scientific notation to standard form, you need to multiply the number by the power of 10 that is written after the number. For example, to convert the number 4.56×1054.56 \times 10^5 to standard form, you would multiply 4.56 by 10510^5 to get 456,000.

Conclusion

In this article, we have answered some frequently asked questions about scientific notation and division. We have covered topics such as what scientific notation is, how to divide numbers in scientific notation, and how to convert numbers from standard form to scientific notation and vice versa. We hope that this article has been helpful in understanding scientific notation and division.