Scientific Notation with Negative Powers of 10

Warm Up Write the following information using scientific notation. The average distance from the Earth to the moon is 240,000 miles. In 2010, the population of California was about 37,250,000. The annual salary of the president of the United States is $400,000. An amoeba is about meters in length. The wavelength of sodium light is centimeters. The volume of a grain of sand is about cubic feet.

You can use scientific notation to express very small quantities by writing the small quantity as the product of a number greater than or equal to 1 and less than 10 times a power of 10 with a negative exponent.

Moving a decimal point one place to the left divides the number by 10. Dividing a number by 10 reduces the exponent by 1. Move decimal points to the left if the number is greater than or equal to 10, move to the right if the number is less than 1.

The weight of one of the smaller species of butterflies was measured at ounces. Write the weight of this butterfly in scientific notation.

How can you write a number that is very close to zero, such as in scientific notation? Count the number of places that the decimal point would have to move to the right to make a number greater than or equal to 1 and less than 10 for the first factor. The second factor is a power of 10 with the exponent equal to -6 to represent the number of places leftward you would need to move the decimal back to its original position.

A single atom of oxygen has a mass of 2.66 × grams. Write 2.66 × in standard notation.

When a number is written in scientific notation, how can you tell right away whether or not it is greater than or equal to 1?

Exit Ticket 1. The weight of an ant is about 1.7 × pounds. Write 1.7 × in standard notation. 2. A bee sting delivers about grams of venom. Write this number in scientific notation. 3. Write 0.77 in scientific notation. 4. Write 1.0 × in standard notation and in words. 5. Is 0.1 × written in scientific notation? Explain.