Scientific Notation expressing a number as the product

Scientific Notation expressing a number as the product of a number between 1 and 10 and a power of ten

93, 000 = 9. 3 × 7 10

10 0 00000000000 0000000000 0 0 00000

0. 000045 = 4. 5 × − 5 10

Example 1 Write the following numbers in scientific notation. a. 1, 670, 000 = 1. 67 × 6 10

Example 1 Write the following numbers in scientific notation. b. 0. 00059 = 5. 9 × − 4 10

To change scientific notation back to standard form, use the exponent to tell how many places to move the decimal point.

Example 2 Write the following numbers in standard form. a. 6. 37 × 105 = 637, 000

Example 2 Write the following numbers in standard form. b. 8. 4 × 10− 3 = 0. 0084

Very Small Numbers micro- millionth 10− 6 nano- billionth 10− 9 pico- trillionth 10− 12 femto- quadrillionth 10− 15 atto- quintillionth 10− 18

Very Large Numbers giga- billion 109 tera- trillion 1012 peta- quadrillion 1015 exa- quintillion 1018

Example 3 Write the following distances in scientific notation. a. the speed of light, about 186, 000 mi. /sec. 1. 86 × 105 mi. /sec.

Example 3 Write the following distances in scientific notation. b. 3. 6 nanometers in meters (a nanometer is one billionth of a meter) 3. 6 × 10− 9 m

Exercise The average distance of Mars from the sun is 227, 000 km. Write this in scientific notation.

Exercise If NASA launched an Earth-to. Mars expedition when the two planets are farthest apart, the mission would have to travel more than 376, 500, 000 km. Write this in scientific notation.

Exercise If NASA launched an Earth-to. Mars expedition when the two planets are closest, approximately how far would it have to travel? Write this in scientific notation.

Exercise If the Earth-to-Mars spaceship averages 35, 000 km/hr. , to the nearest hour, how long would it take to travel from Earth to Mars when they are farthest apart? State your answer in hours, and then convert it to days (round to the nearest whole number).