Question

Multiply (2.3 × 10–5)(3.1 × 101

Answer 1

To multiply numbers in scientific notation, first multiply the numbers that do not have a base of 10 and then add the exponents of the bases of 10. Essentially:

`(a \cdot 10^b)(c \cdot 10^d)`

`(a \cdot c) \cdot (10^((b + d)))`

In this case, we see that the numbers that do not have bases of 10 are 2.3 and 3.1. Multiplying these numbers gives us:

`2.3 \cdot 3.1 = 7.13`

The exponents on the bases of 10 are -5 and 1. Adding these exponents gives us -4, which we can add to our final base of 10.

Thus, our answer is:

`\boxed{7.13 \cdot 10^(-4)}`

Answer 2

5,635.8

Explanation:

We are to multiply (2.3 × 10 - 5)(3.1 × 101)

Applying PEMDAS;

We solve the brackets first and multiply to get:

(23 - 5)(313.1)

Subtracting gives;

(18)(313.1)

Finally; 18 × 313.1 = 5,635.8