Mohammed copied this problem into his notebook.
(3.4x10^5)(3.8x10^-9)
A. Use the associative and commutative properties to rearrange the factors.
B. Find the product and write it in standard form.
3.4 * 3.8 * 10^(5-9)
12.92 * 10^-4
1.292 * 10^-3 (or 0.001292)
Why is the final answer 1.292 *10^-3 instead of 10^-6? isn't 0.001292 = 10^-6?
because 5 and 9 are the two exponents and they are being subtracted by each other and 5-9 is -3
A. To rearrange the factors using the associative and commutative properties, we can rewrite the problem as follows:
(3.4 x 10^5)(3.8 x 10^-9) = (3.4)(3.8) x (10^5)(10^-9)
Using the commutative property, we can switch the order of multiplication:
= (3.8)(3.4) x (10^-9)(10^5)
Using the associative property, we can group the numbers together:
= (3.8 x 3.4) x (10^-9 x 10^5)
Now the factors are rearranged, and we can move on to finding the product and writing it in standard form.
B. To find the product of (3.8 x 3.4) and (10^-9 x 10^5), we can multiply the numerical parts separately and the powers of 10 separately:
(3.8 x 3.4) = 12.92
(10^-9 x 10^5) = 10^(-9 + 5) = 10^-4
Now, we can multiply the numerical part (12.92) by the power of 10 (10^-4):
12.92 x 10^-4
To write this in standard form, we need to move the decimal point four places to the left because of the negative exponent:
= 0.001292
Therefore, the product of (3.4x10^5)(3.8x10^-9) is 0.001292 in standard form.