Problem

Calculate: \[ \left(-2.5 \times 10^{-3}\right)\left(-3.0 \times 10^{1}\right) \] Write your answer in scientific notation. $\square$ $\times 10$

Solution

Step 1 :The question is asking for the product of two numbers, both of which are in scientific notation. To solve this, we will multiply the two numbers as if they were regular decimal numbers, and then adjust the exponent of 10 accordingly.

Step 2 :The product of two numbers in scientific notation is found by multiplying the two numbers (ignoring the powers of 10 for now) and then adding the exponents of 10. In this case, the two numbers are -2.5 and -3.0, and the exponents of 10 are -3 and 1.

Step 3 :The product of -2.5 and -3.0 is 7.5 (ignoring the negative signs for now), and the sum of -3 and 1 is -2. So, the product of the two numbers in scientific notation is \(7.5 \times 10^{-2}\).

Step 4 :However, in scientific notation, the number before the \(x 10^{}\) part should be between 1 and 10. So, we need to adjust the number and the exponent of 10 to fit this format.

Step 5 :We can do this by moving the decimal point in 7.5 one place to the left, which gives 0.75. To compensate for this, we need to increase the exponent of 10 by 1, which gives -1.

Step 6 :So, the final answer in scientific notation is \(0.75 \times 10^{-1}\).

Step 7 :The product of \((-2.5 \times 10^{-3})\) and \((-3.0 \times 10^{1})\) in scientific notation is \(\boxed{0.75 \times 10^{-1}}\).

From Solvely APP
Source: https://solvelyapp.com/problems/vKaqOEfNcK/

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