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2003-B: Scientific Notation 1: Scientific to Standard Notation

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2003-B: Scientific Notation 1: Scientific to Standard Notation

BACK to Ladder Scientific Notation and Orders of Magnitude

In science, we typically represent numbers in a form called scientific notation. In scientific notation, numbers have two parts: the significant figures and the order of magnitude. In the following example, the significant figures are 3.45 and the order of magnitude is +6.

Sometimes, the significant figures are referred to as the coefficient and the order of magnitude is referred to as the exponent. In this class, I prefer to use the term "significant figures" and "order of magnitude."

All of the numbers you are used to writing, such as 10, 28, 415891, are called numbers in standard notation.

Converting Scientific Notation to Standard Notation

Questions:

Convert each number to standard notation.

  1. \( 3.45 \times 10^4 = \)
  2. \( 4.23 \times 10^7 = \)
  3. \( 9.12 \times 10^2 = \)
  4. \( 4.87 \times 10^5 = \)
  5. \( 8.25 \times 10^6 = \)
  6. \( 2.45 \times 10^0 = \)
  7. \( 2.45 \times 10^1 = \)
  8. \( 3.89 \times 10^0 = \)
  9. \( 4.23 \times 10^{-3} = \)
  10. 3.28E-8
  11. 6.78E-5
  12. 3.85e-4
  13. 5.28e-7
  14. 3.42E5
  15. 4.23E2
  16. What do we call the digits at the beginning of a scientific notation number?
  17. What do we call the exponent in a scientific notation number?

Answers:

    BACK to Ladder Scientific Notation and Orders of Magnitude

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