Converting Scientific Notation to Decimal Equivalents

Oct 13, 2025 by wbrum.org 106 views

Scientific notation is a way of expressing very large or very small numbers in a compact form. It consists of a number between 1 and 10 multiplied by a power of 10. In this article, we will explore the concept of scientific notation and how to convert numbers from scientific notation to decimal equivalents.

What is Scientific Notation?

Scientific notation is a method of expressing numbers in the form a × 10^n, where a is a number between 1 and 10, and n is an integer. This notation is commonly used in mathematics, physics, and engineering to represent very large or very small numbers in a compact form.

Converting Scientific Notation to Decimal Equivalents

To convert a number from scientific notation to a decimal equivalent, we need to multiply the number by the power of 10. For example, if we have the number 3.4 × 10^2, we can convert it to a decimal equivalent by multiplying 3.4 by 10^2, which is equal to 3.4 × 100 = 340.

Converting $$8.7 \times 10^{-2}$$ to a Decimal Equivalent

Now, let's apply this concept to the given problem. We need to convert the number $$8.7 \times 10^{-2}$$ to a decimal equivalent. To do this, we need to multiply 8.7 by 10^(-2), which is equal to 8.7 × 0.01 = 0.087.

Analyzing the Options

Now that we have converted the number $$8.7 \times 10^{-2}$$ to a decimal equivalent, let's analyze the options given in the problem.

A. 0.08: This option is incorrect because it is not equal to $$8.7 \times 10^{-2}$$.
B. 0.087: This option is correct because it is equal to $$8.7 \times 10^{-2}$$.
C. 0.87: This option is incorrect because it is not equal to $$8.7 \times 10^{-2}$$.
D. 0.0087: This option is incorrect because it is not equal to $$8.7 \times 10^{-2}$$.

Conclusion

In conclusion, the correct answer to the problem is B. 0.087. This is because it is the decimal equivalent of $$8.7 \times 10^{-2}$$.

Key Takeaways

Scientific notation is a method of expressing numbers in the form a × 10^n, where a is a number between 1 and 10, and n is an integer.
To convert a number from scientific notation to a decimal equivalent, we need to multiply the number by the power of 10.
The decimal equivalent of $$8.7 \times 10^{-2}$$ is 0.087.

Frequently Asked Questions

What is scientific notation?
How do I convert a number from scientific notation to a decimal equivalent?
What is the decimal equivalent of $$8.7 \times 10^{-2}$$?

Answers

Scientific notation is a method of expressing numbers in the form a × 10^n, where a is a number between 1 and 10, and n is an integer.
To convert a number from scientific notation to a decimal equivalent, we need to multiply the number by the power of 10.
The decimal equivalent of $$8.7 \times 10^{-2}$$ is 0.087.
Scientific Notation Q&A ==========================

Frequently Asked Questions

What is scientific notation?

Answer: Scientific notation is a method of expressing numbers in the form a × 10^n, where a is a number between 1 and 10, and n is an integer. This notation is commonly used in mathematics, physics, and engineering to represent very large or very small numbers in a compact form.

How do I convert a number from scientific notation to a decimal equivalent?

Answer: To convert a number from scientific notation to a decimal equivalent, you need to multiply the number by the power of 10. For example, if you have the number 3.4 × 10^2, you can convert it to a decimal equivalent by multiplying 3.4 by 10^2, which is equal to 3.4 × 100 = 340.

What is the decimal equivalent of $$8.7 \times 10^{-2}$$?

Answer: The decimal equivalent of $$8.7 \times 10^{-2}$$ is 0.087. This is because you need to multiply 8.7 by 10^(-2), which is equal to 8.7 × 0.01 = 0.087.

How do I convert a decimal equivalent to scientific notation?

Answer: To convert a decimal equivalent to scientific notation, you need to move the decimal point to the left or right until you have a number between 1 and 10, and then multiply or divide by 10 to get the correct power of 10. For example, if you have the decimal equivalent 340, you can convert it to scientific notation by moving the decimal point 2 places to the left, which gives you 3.4 × 10^2.

What are some common examples of scientific notation?

Answer: Some common examples of scientific notation include:

3.4 × 10^2 (which is equal to 340)
2.5 × 10^3 (which is equal to 2500)
1.8 × 10^4 (which is equal to 18000)
4.2 × 10^5 (which is equal to 420000)

How do I add or subtract numbers in scientific notation?

Answer: To add or subtract numbers in scientific notation, you need to make sure that the powers of 10 are the same. If they are not the same, you need to adjust the numbers by multiplying or dividing by 10 to get the correct power of 10. For example, if you have the numbers 3.4 × 10^2 and 2.5 × 10^2, you can add them by adding the numbers and keeping the same power of 10, which gives you 5.9 × 10^2.

How do I multiply or divide numbers in scientific notation?

Answer: To multiply or divide numbers in scientific notation, you need to multiply or divide the numbers and add or subtract the powers of 10. For example, if you have the numbers 3.4 × 10^2 and 2.5 × 10^3, you can multiply them by multiplying the numbers and adding the powers of 10, which gives you 8.5 × 10^5.

What are some real-world applications of scientific notation?

Answer: Scientific notation has many real-world applications, including:

Calculating large or small numbers in physics and engineering
Expressing numbers in a compact form in mathematics and science
Performing calculations with very large or very small numbers in finance and economics
Representing numbers in a standard form in computer programming and data analysis

How do I use scientific notation in everyday life?

Answer: You can use scientific notation in everyday life by applying it to real-world problems and calculations. For example, if you need to calculate the area of a large room, you can use scientific notation to express the dimensions of the room in a compact form. Similarly, if you need to calculate the cost of a large purchase, you can use scientific notation to express the cost in a compact form.