7.1 The student will compare, order, and determine equivalent relationships between fractions, decimals, and percents, including use of scientific notation for numbers greater than 10.

Answers

  • The numbers are …
  • the speed of light!
  • the mass of a dust particle!
  • the mass of a proton!
  • the revolutions of a turntable!
  • the volume of a raindrop!

Directions1

  • To write a number in scientific notation:
  • Put the decimal after the first digit and drop the zeroes.
  • In the number 123,000,000,000 The coefficient will be 1.23
  • To find the exponent count the number of places from the decimal to the end of the number.
  • In 123,000,000,000 there are 11 places. Therefore we write 123,000,000,000 as: 1.23 x 1011.

Directions 2

  • Convert from Scientific Notation to Real Number:
  • 5.14 x 105 = 514000.0
  • Scientific notation consists of a base (here 5.14) multiplied by 10 raised to an exponent (here 5). To convert to a real number, start with the base and multiply by 5 tens like this: 5.14 x 10 x 10 x 10 x 10 x 10 = 514000.0. Multiplying by tens is easy: one simply moves the decimal point in the base (5.14) 5 places to the right, adding extra zeroes as needed.

Hands-On Activities

  • Practice on-line, converting scientific notation to real numbers and from real numbers to scientific notation.
  • Converting Practice

Other Web Sites

  • Shodor
  • Why use scientific notation?
  • Janus provides some notes on converting numbers into scientific notation as well as practice problems that convert numbers into scientific notation and from scientific notation to standard form.
  • DEAD LINK: Here are some notes on converting numbers into scientific notation. There are practice problems at the end of the lesson with feedback. Studyzone

Puzzles and Problems

  1. There are 365.25 days in a year and 1440 minutes in a day.Determine how many minutes there are in a year and express your answer in scientific notation.
  2. The Andromeda Galaxy (the closest one to our Milky Way galaxy) contains at least 200,000,000,000 stars. On the other hand, the weight of an alpha particle, which is emitted in the radioactive decay of Plutonium-239, is 0.000,000,000,000,000,000,000, 000,006,645 kilograms.Express both of these numbers in scientific notation.

Lesson 7-1: Project

  • Do you recognize these numbers? - NEEDS UNIT UPDATES
  • 300,000,000 m/sec.
  • 0.000 000 000 753 kg
  • 0.00000000000000000000000167
  • 2750062
  • 0.001297
  • (You can find the answers on the right side of the page.)

Scientists have developed a shorter method to express very large or very small numbers. This method is called scientific notation.

The number 123,000,000,000 in scientific notation is written as: 1.23 x 1011. The first number 1.23 is called the coefficient. It must be greater than or equal to 1 and less than 10. The second number is called the base . It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x 1011 the number 11 is referred to as the exponent or power of ten.

Exponents are often expressed using other notations. The number 123,000,000,000 can also be written as: 1.23E+11 or as 1.23 X 1011. For small numbers we use a similar approach. Numbers smaller than 1 will have a negative exponent. A millionth of a second is: 0.000001 seconds or 1.0E-6 or 1.0 x 10–6.