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

1 Answer
Ernest Z.
Sep 9, 2016

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"#

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