Question

A grain of sand has a mass of approximately .00000003 grams. How would this number be expressed in scientific notation?

Answer 1

In scientific notation, the mass is `3× 10^"-8"color(white)(l) "g"`.

Explanation:

Scientific notation is a way of writing very large and very small numbers.

A number in scientific notation has the form `N× 10^a`, where `N` is a number between 1 and 10, and `a` is a positive or negative integer.

To convert to scientific notation, you move the decimal point until the new form is a number between 1 and 10 (`N`) and then record the exponent (`a`) as the number of places the decimal point was moved.

If you move the decimal to the right, the exponent is negative.

Express `"0.000 000 03 g"` in scientific notation.

Step 1. Move the decimal place to the right to create a new number between 1 and 10.

This gives `N = 3`.

Step 2. Count the number of times you moved the decimal.

You moved the decimal 8 places to the right.

That means the exponent `a = "-8"`.

Step 3. Write the number in scientific notation.

`"0.000 000 03 g" = 3 × 10^"-8"color(white)(l) "g"`