a:6.7 x 10^2
b:8.4 x 10^5
which one is bigger and why show work.
put this: "Negative exponents usually add up to .00000 and i think positive exponents will add up to random numbers and then the decimals at the end if their any" into more bigger words
To compare the two numbers, we need to convert them to decimal form. In scientific notation, the number before the multiplication symbol represents the coefficient, and the number after the multiplication symbol represents the base raised to a certain power.
a: 6.7 x 10^2 = 6.7 * 100 = 670
b: 8.4 x 10^5 = 8.4 * 100000 = 840000
By converting both numbers, we can see that b (840,000) is bigger than a (670). This is because 840,000 is a larger value than 670.
Regarding your statement, "Negative exponents usually add up to .00000, and I think positive exponents will add up to random numbers and then the decimals at the end if there are any," it can be expressed more precisely as follows:
Negative exponents generally indicate that the base is divided by 1 followed by several zeros. For example, a number in scientific notation like 5 x 10^-4 would be converted to a decimal as 0.0005. When a base is raised to a positive exponent, it results in the base multiplied by itself multiple times, leading to larger values. The decimal values at the end depend on the specific calculation and may vary.
now put this "a: 6.7 x 10^2 = 6.7 * 100 = 670
b: 8.4 x 10^5 = 8.4 * 100000 = 840000
By converting both numbers, I can see that B is bigger than A. This is because 840,000 is a larger value than 670." in simpler words
Let's simplify comparing the two numbers using their decimal forms.
For a: 6.7 x 10^2 = 6.7 multiplied by 100 = 670
For b: 8.4 x 10^5 = 8.4 multiplied by 100,000 = 840,000
When we convert both numbers to decimals, we can see that b (840,000) is a bigger number compared to a (670). This is because 840,000 is larger than 670.
To determine which number is bigger, we need to compare the values of the exponents. Let's consider the given numbers:
a: 6.7 x 10^2
b: 8.4 x 10^5
In both a and b, the base numbers (6.7 and 8.4) are positive. As you mentioned, positive exponents indicate larger values, and negative exponents indicate smaller values.
In a, the exponent is 2, which means we multiply the base number (6.7) by 10 squared (10^2). This gives us 6.7 * 100 = 670.
In b, the exponent is 5, so we multiply the base number (8.4) by 10 to the power of 5 (10^5). This gives us 8.4 * 100,000 = 840,000.
Comparing the results:
a: 670
b: 840,000
We can see that b is greater than a because 840,000 is larger than 670. Therefore, b is the bigger number.
Regarding your request for bigger words, here is an expanded explanation:
"Negative exponents typically result in very small numbers, often close to zero, such as 0.00000. On the other hand, positive exponents can yield larger numerical values, which may not follow a specific pattern or predefined set of decimals at the end."
I hope this clarifies the concepts for you! If you have any additional questions, feel free to ask.