36 Scientific Notation

Scientific Notation

Scientific notation is used to express extremely large or extremely small numbers efficiently. The main idea is to write the number you want as a number between 1 and 10 multiplied by an integer power of 10.

Fill in the blanks in the table below. Write the decimal form of the number given in scientific notation. Then give the calculator’s notation for the scientific notation. This is the only time you should write this calculator notation. Calculator notation is not acceptable in your written work; use a human language! The last column is for a word name for the number. In a few rows, you will write the scientific notation yourself.

Scientific Decimal Notation Calculator Word name for the notation notation number One billion one billion dollars dollars 1.0 ×10 9 dollars

One year 3.16 ×10 7 seconds Distance from earth to moon 3.8 ×10 8 meters 6.24 ×10 23 Mass of Mars 624 sextillion kg kilograms 1.0 ×10 -9 Nanosecond seconds Speed of tv 3.0 ×10 8 signals meters/second Atomic mass 1.66 ×10 -27 Just say, “1.66 ×10 -27 unit kilograms kg”! Light year 6×10 12 miles

Light year 9.5 ×10 15 meters One billion light years meters Parsec 3.1 ×10 16 meters Megaparsec 10 6 parsecs

Megabyte = 220 = 1,048,576 20 2 bytes bytes bytes Micron One millionth of a meter The number of About one hundred stars in the billion Milky Way Diameter of a 7.5 ×10 -14 carbon-12 meters atom

Rosalie A. Dance and James T. Sandefur, 2004

This material is based upon work supported by the National Science Foundation under Grant No. 0087068. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Distance from 1.5 ×10 11 Earth to Sun meters

Rosalie A. Dance and James T. Sandefur, 2004

Teaching Guide for Scientific Notation

The table is intended for fun as well as for gaining awareness and understanding of both scientific notation and large and small numbers. It is not necessary for any student to do all of it. This might be an opportunity for students to share results rather than engage in getting all results together as usual. Of course, each student should be sure (s)he understands all the numbers.

Scientific Decimal Notation Calculator Word name for the notation -ese for number sci. notat. One billion $1,000,000,000 1E9 one billion dollars dollars 1.0 ×10 9 dollars One year 3.16 ×10 7 31,600,000 seconds 3.16E7 Thirty one million six seconds hundred thousand sec. Distance from 380,000,000 meters 3.8E8 Three hundred eighty earth to moon 3.8 ×10 8 meters million meters 23 Mass of Mars 6.24 ×10 624,000,000,000,000,000,000,000 kg 6.24E23 624 sextillion kg kilograms Nanosecond 1.0 ×10 -9 0.000000001 second 1E-9 1 billionth of a second seconds Speed of tv 3.0 ×10 8 300,000,000 m/sec 3E8 Three hundred million signals meters/second meters per second -27 -27 Atomic mass 1.66 ×10 0.00000000000000000000000000166 1.66E-27 Just say, “1.66 ×10 unit kilograms kg kg”! Light year 6×10 12 miles 6,000,000,000,000 mi. 6E12 Six trillion miles Light year 9.5 ×10 15 9,500,000,000,000,000 m 9.5E15 Nine quadrillion five meters hundred trillion meters One billion light 9.5 ×10 24 9,500,000,000,000,000,000,000,000 m 9.5E24 Nine septillion five years meters hundred sextillion m. Parsec 3.1 ×10 16 31,000,000,000,000,000 m 3.1E16 Thirtyone quadrillion meters m Megaparsec 10 6 parsecs 1,000,000 parsecs 1E6 One million parsecs 6 Megabyte = ≈ 1.05 ×10 220 = 1,048,576 bytes 1.05E6 One million,forty eight 220 bytes bytes thousand, five hundred seventy six Micron 10 -6 meters 0.000001 m 1E-6 One millionth of a meter The number of 10 11 stars 100,000,000,000,000 1E11 About one hundred stars in the stars billion Milky Way Diameter of a 7.5 ×10 -14 0.000000000000075 m 7.5E-14 Seventy five carbon-12 meters quadrillionths of a atom meter Distance from 1.5 ×10 11 150,000,000,000 m 1.5E11 One hundred fifty Earth to Sun meters billion meters

Rosalie A. Dance and James T. Sandefur, 2004