What is the correct expression of 34,000 x 96,000 using scientific notation?
The Correct Answer and Explanation is :
To express the product of (34,000) and (96,000) in scientific notation, we first need to calculate the product:
[
34,000 \times 96,000 = 3,264,000,000
]
Now, we will convert (3,264,000,000) into scientific notation. Scientific notation expresses numbers as a product of a coefficient and a power of ten. The coefficient must be between (1) and (10).
To convert (3,264,000,000):
- Identify the Coefficient: Start with (3,264,000,000) and move the decimal point to the left until there is only one non-zero digit to the left of the decimal. In this case, moving the decimal point (9) places to the left gives us: [
3.264
] - Count the Places Moved: Since we moved the decimal point (9) places, we represent this as a power of ten: [
3.264 \times 10^9
]
Thus, the expression of (34,000 \times 96,000) in scientific notation is:
[
3.264 \times 10^9
]
Explanation
Scientific notation is a convenient way to handle very large or very small numbers, making calculations easier and reducing the likelihood of errors in significant digits. It is especially useful in scientific and engineering contexts, where such numbers frequently arise.
In scientific notation, the base (10) exponent indicates the magnitude of the number. A positive exponent, like (10^9), shows that the number is large, specifically in the billions. Conversely, a negative exponent would indicate a number smaller than one.
When performing operations like multiplication or division with numbers in scientific notation, you can simplify the process by manipulating the coefficients and the powers of ten separately. For example, when multiplying two numbers in scientific notation, you multiply the coefficients and add the exponents.
This method enhances clarity, especially when communicating complex values or performing calculations across various scientific disciplines.