Scientific Notation Rules

Scientific Notation Rules

Scientific Notation

• • Used when dealing with very large or very small numbers.

    • Form: A.BC x 10d

    • A.BC… is the “ones” term

    • 10d is the “tens” or “exponent” term

  • Converting between decimal and scientific notation

    • Move the decimal to increase or decrease the “ones” term to be greater than 1 but less than 10.

    • Multiply “ones” term by 10d, where d is the number of spaces the decimal was moved.

  • Examples

    • 5,089,000,000 = 5.089 x 109

    • 0.0000000672 = 6.72 x 10-8

Addition/subtraction in scientific notation

• • Before adding the “ones” terms, convert all “tens” terms to the same exponential value.

  • Example: (3.01 x 1022) + (1.19 x 1023) + (9.8 x 1021) =

    • First convert all values to same exponent value, say 22:

      • (3.01 x 1022) + (11.9 x 1022) + (0.980 x 1022) = (15.890 x 1022)

    • Round using the addition rule:

      • 15.9 x 1022

    • Adjust to correct scientific notation:

      • 1.59 x 1023

  • Note: With addition/subtraction you round to significant figures before adjusting for the correct scientific notation.

Multiplication/division in scientific notation

• • Multiply all the “ones” terms first

  • Multiply the “tens” terms by ADDING the exponents together.

  • Divide the “tens” terms by SUBTRACTING the exponents.

  • Examples

    • Multiplication:

      • (3.4 x 1014)(6.3 x 1012) = 21.42 x 1026 = 21 x 1026

      • (3.4 x 1014)(6.3 x 10-12) = 21.42 x 102 = 21 x 102

    • Division:

      • 3.4 x 10¹⁴ / 6.3 x 10¹² = 0.539 x 102 = 5.4 x 101 = 54

      • 3.4 x 10¹⁴ / 6.3 x 10^-12 =0.539 x 1026 = 5.39 x 1025 = 5.4 x 1025

  • Note: With multiplication/division you adjust for correct scientific notation and then round to significant figures