What Is The Value Of $12.5 \times 10^7$?A) 12.5000000 B) $125,000,000$ C) $ 1 , 250 , 000 1,250,000 1 , 250 , 000 [/tex] D) 1.2500000
Understanding the Concept of Scientific Notation
Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It involves expressing a number as a product of a number between 1 and 10 and a power of 10. In the given problem, we are asked to find the value of $12.5 \times 10^7$. To solve this, we need to understand the concept of scientific notation and how to multiply numbers in this form.
Multiplying Numbers in Scientific Notation
When multiplying numbers in scientific notation, we multiply the coefficients (the numbers in front of the powers of 10) and add the exponents of the powers of 10. This is based on the rule that $a^m \times a^n = a^{m+n}$.
Applying the Rule to the Given Problem
In the given problem, we have $12.5 \times 10^7$. To find the value, we multiply the coefficient 12.5 by the power of 10, which is $10^7$. Using the rule mentioned above, we can write this as:
Simplifying the Expression
Now, we can simplify the expression by multiplying the coefficient 12.5 by the power of 10, $10^7$. This gives us:
Conclusion
Therefore, the value of $12.5 \times 10^7$ is $125,000,000$.
Understanding the Options
Let's analyze the options given:
- A) 12.5000000: This is the original number 12.5, not the result of multiplying it by $10^7$.
- B) $125,000,000$: This is the correct result of multiplying 12.5 by $10^7$.
- C) $: This is not the correct result of multiplying 12.5 by $10^7$.
- D) 1.2500000: This is the original number 1.25, not the result of multiplying 12.5 by $10^7$.
Final Answer
The final answer is B) $125,000,000$.
Frequently Asked Questions
Q: What is the concept of scientific notation?
A: Scientific notation is a way of expressing very large or very small numbers in a more manageable form.
Q: How do we multiply numbers in scientific notation?
A: We multiply the coefficients (the numbers in front of the powers of 10) and add the exponents of the powers of 10.
Q: What is the value of $12.5 \times 10^7$?
A: The value of $12.5 \times 10^7$ is $125,000,000$.
Q: Why is option A incorrect?
A: Option A is the original number 12.5, not the result of multiplying it by $10^7$.
Q: Why is option C incorrect?
A: Option C is not the correct result of multiplying 12.5 by $10^7$.
Q: Why is option D incorrect?
A: Option D is the original number 1.25, not the result of multiplying 12.5 by $10^7$.
Conclusion
In conclusion, the value of $12.5 \times 10^7$ is $125,000,000$. This is based on the concept of scientific notation and the rule for multiplying numbers in this form.
Understanding Scientific Notation
Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It involves expressing a number as a product of a number between 1 and 10 and a power of 10. In this article, we will answer some frequently asked questions about scientific notation.
Q&A
Q: What is the concept of scientific notation?
A: Scientific notation is a way of expressing very large or very small numbers in a more manageable form. It involves expressing a number as a product of a number between 1 and 10 and a power of 10.
Q: How do we express a number in scientific notation?
A: To express a number in scientific notation, we need to write it as a product of a number between 1 and 10 and a power of 10. For example, the number 456,789 can be written as 4.56789 × 10^5.
Q: How do we multiply numbers in scientific notation?
A: We multiply the coefficients (the numbers in front of the powers of 10) and add the exponents of the powers of 10. For example, (3.4 × 10^2) × (2.5 × 10^3) = 8.5 × 10^5.
Q: How do we divide numbers in scientific notation?
A: We divide the coefficients (the numbers in front of the powers of 10) and subtract the exponents of the powers of 10. For example, (3.4 × 10^2) ÷ (2.5 × 10^3) = 1.36 × 10^-1.
Q: How do we add or subtract numbers in scientific notation?
A: We need to make sure that the powers of 10 are the same before we can add or subtract the coefficients. For example, (3.4 × 10^2) + (2.5 × 10^2) = 5.9 × 10^2.
Q: What is the difference between scientific notation and standard notation?
A: Scientific notation is a way of expressing very large or very small numbers in a more manageable form, while standard notation is the usual way of writing numbers.
Q: Why is scientific notation useful?
A: Scientific notation is useful because it allows us to express very large or very small numbers in a more manageable form, making it easier to perform calculations and understand the numbers.
Q: How do we convert a number from standard notation to scientific notation?
A: To convert a number from standard notation to scientific notation, we need to move the decimal point to the left or right until we have a number between 1 and 10, and then multiply or divide by a power of 10.
Q: How do we convert a number from scientific notation to standard notation?
A: To convert a number from scientific notation to standard notation, we need to multiply or divide the coefficient by the power of 10, and then move the decimal point to the left or right.
Conclusion
In conclusion, scientific notation is a useful way of expressing very large or very small numbers in a more manageable form. It involves expressing a number as a product of a number between 1 and 10 and a power of 10. We hope that this article has helped to answer some of the frequently asked questions about scientific notation.