Question

What type of number is -296.2i

Choose all answers that apply:

Answer 1

The number -296.2i is a pure imaginary number. Scientific notation is used to express very large or small numbers conveniently, and involves moving the decimal point to create a new number between 1 and 10 multiplied by a power of 10.

Step-by-step explanation:

The type of number -296.2i is known as a pure imaginary number. Imaginary numbers are numbers that can be written as a real number multiplied by the imaginary unit i, which is the square root of -1. This type of number is used in advanced mathematics to represent quantities that cannot be measured on the real number line, such as the solutions to equations that do not have real solutions.

Expressing Numbers in Scientific Notation

To express numbers in scientific notation, you write them as the product of a number between 1 and 10 and a power of 10. Here are the steps to convert the given numbers:

• For -890,000: Move decimal 5 places to the left to get -8.9 × 105
• For 602,000,000,000: Move decimal 11 places to the left to get 6.02 × 1011
• For 0.0000004099: Move decimal 7 places to the right to get 4.099 × 10-7
• For 0.000000000000011: Move decimal 14 places to the right to get 1.1 × 10-14

Answer 2

The number -296.2i is a complex number because it contains the imaginary unit 'i'. Scientific notation is used to express large or small numbers in a format of a number between 1 and 10 multiplied by a power of 10. Examples include converting -890,000 to -8.9 x 10^5 and 602,000,000,000 to 6.02 x 10^11.

Step-by-step explanation:

The number -296.2i is a complex number because it includes the imaginary unit 'i', which is the square root of -1. The format of a complex number is usually expressed as a + bi, where 'a' is the real part and 'bi' is the imaginary part. In this case, there is no real part (it would be 0), and the imaginary part is -296.2i.

Now, let's look at how to express numbers in scientific notation:

1. -890,000 would be -8.9 x 105.
2. 602,000,000,000 becomes 6.02 x 1011.
3. For the number 0.0000004099, it is 4.099 x 10-7.
4. The number 0.000000000000011 in scientific notation is 1.1 x 10-14.
5. Writing 0.00656 in scientific notation gives 6.56 x 10-3.
6. 65,600 in scientific notation is 6.56 x 104.