The smallest number obtained by multiplying two values given in standard form is calculated by multiplying the smallest coefficients and adding the exponents in scientific notation. The result is 3.0 × 10⁹.
To find the smallest number that can be obtained by multiplying two of the given values in standard form, we should look for the values with the smallest exponents when written in scientific notation. Standard form and scientific notation both allow us to represent very large or very small numbers in a more concise and manageable way. We have the numbers 6 × 10³, 5 × 10⁵, 4.5 × 10⁵, and 1×10⁶. Multiplying two numbers in scientific notation involves multiplying the coefficients (the numbers out front) and then adding the exponents of the 10s.
The smallest product would come from the smallest coefficients and the smallest exponents, which in this case would be 6 × 10³ and 5 × 10⁵. Multiplying these together, we have:
(6 × 5) × (10³ × 10⁵) = 30 × 10³+⁵ = 30 × 10⁸
However, 30 is not between 1 and 10, so we need to adjust this to proper scientific notation which gives us:
3.0 × 10× 10⁸ = 3.0 × 10⁹
So the smallest number that can be made by multiplying any two of these values is 3.0 × 10⁹.