Question

a. Will the exponent of the power of 10 be positive or negative when writing0.00000008 in scientific notation? How do you know?b. Will the exponent of the power of 10 be positive or negative when writing20 billion in scientific notation? How do you know?

Answer 1

Scientific Notation

We use scientific notation to express in short terms numbers too large or too small.

When a number is too small like 0.00000008 we prefer to write it in the form:

`a\cdot10^b`

Where a is a number between 1 (inclusive) and 10 (non-inclusive).

The value of b is a power of 10 that will be negative if the original number is less than 1 and positive if it's greater or equal to 10.

Now we are required to explain why is that.

a. The number 0.00000008 can be expressed like:

`(8)/(100,000,000)`

Expressing the denominator as a power of 10:

`(8)/(100,000,000)=(8)/(10^8)`

Applying the properties of exponents:

`(8)/(100,000,000)=(8)/(10^8)=8\cdot10^(-8)`

The exponent is negative because we wrote the base 10 in the numerator.

b. The number 20 billion is 20,000,000,000

This time the number is greater than 1 and the exponent of the base 10 will be positive:

`20,000,000,000=2\cdot10,000,000,000=2\cdot10^(10)`