Final answer:
To find the product of x and y in standard scientific notation, multiply the coefficients and add the exponents, ensuring that the coefficient of the result is between 1 and 10.
Step-by-step explanation:
You are asked to find the product of two numbers, x and y, expressed in scientific notation, given that x = a x 10⁽¹ and y = b x 10⁻¹, and where the product ab is between 100 and 1000. To do this, you'll need to use the rules for multiplying numbers in scientific notation.
When multiplying two numbers in scientific notation, multiply the coefficients (a and b) and add the exponents (m and n). In scientific notation, the product will be expressed as (a x b) x 10⁽¹⁻¹. Since 100 < ab < 1000, ab will be a number with either two or three digits before the decimal point, which means it's already in the format required for the coefficient in standard scientific notation.
So, xy will have the form of some number between 100 and 1000 multiplied by 10 raised to the power of m+n. For example, if a is 4.5, and we have x = 4.5 x 10⁶, and if for example, b is 220 and n is 1, we have y = 220 x 10¹, then the product of x and y would be xy = (4.5 x 220) x 10⁶⁰¹ = 990 x 10⁷, which can be further refined to 9.9 x 10¹⁰, conforming to the rules of scientific notation where the coefficient (9.9 in this case) is between 1 and 10.