Question

Describe the procedure for multiplying two numbers in scientific notation.

Then find the product of (5.8 x 10-⁴)(8x 10-⁵).

Answer 1

To multiply numbers in scientific notation, multiply the coefficients, add the exponents, and ensure the product is in correct scientific notation format. The product of (5.8 x 10^-4) and (8 x 10^-5) is 4.64 x 10^-8.

Step-by-step explanation:

To multiply two numbers in scientific notation, you first multiply the coefficients (the numbers out front) and then add the exponents of the powers of ten. When performing this operation, you must ensure that the product of the coefficients is also expressed in proper scientific notation, which means it should have only one non-zero digit to the left of the decimal point. Here is a step-by-step procedure:

1. Multiply the coefficients of the two numbers.
2. Add the exponents of the powers of ten.
3. Adjust the product of the coefficients to ensure it follows the format of scientific notation, if necessary.

Now let's find the product of (5.8 x 10^-4)(8 x 10^-5).

First, multiply the coefficients: 5.8 x 8 = 46.4.

Next, add the exponents: (-4) + (-5) = -9.

The result is 46.4 x 10^-9. However, since 46.4 is not in the proper scientific notation format, we must adjust it to 4.64 x 10^-8 by moving the decimal point one place to the left and compensating by increasing the exponent of ten by one.

Therefore, the product of the two numbers is 4.64 x 10^-8.