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Note: If the numbers start with the same exponents, their coefficients can be added, but be careful--the answer might need to be converted to scientific notation.

Example 1: 2.456×105 +6.0034×108 = ?

  1. 8 - 5 = 3. The smaller exponent must be increased by 3.
  2. 2.456×105 = 0.002456×108
  3. 0.002456×108 +6.0034×108 = 6.005856×108
  4. 6.005856×108 is in scientific notation.
Thus, 2.456×105 +6.0034×108 = 6.005856×108.

Example 2: 5.10802×103 -6.1×10-2 = ?

  1. 3 - (-2) = 5. The smaller exponent must be increased by 5.
  2. 6.1×10-2 = 0.000061×103
  3. 5.10802×103 -0.000061×103 = 5.107959×103
  4. 5.107959×103 is in scientific notation.
Thus, 5.10802×103 -6.1×10-2 = 5.107959×103.

Example 3: 3.5×1018 + 5.3×1012 = ?

  1. 18 - 12 = 6. The smaller exponent must be increased by 6.
  2. 5.3×1012 = 0.0000053×1018
  3. 3.5×1018 + 0.0000053×1018 = 3.5000053×1018
  4. 3.5000053×1018 is in scientific notation.
Thus, 3.5×1018 + 5.3×1012 = 3.5000053×1018.

Example 4: 4.801×103 -2.2×107 = ?

  1. 7 - 3 = 4. The smaller exponent must be increased by 4.
  2. 4.801×103 = 0.0004801×107
  3. 0.0004801×107 -2.2×107 = - 2.1995199×107
  4. -2.1995199×107 is in scientific notation.
Thus, 4.801×103 -2.2×107 = - 2.1995199×107.

Example 5.1.4×10-5 -5.67×10-6 = ?

  1. -5 - (-6) = 1. The smaller exponent must be increased by 1.
  2. 5.67×10-6 = 0.567×10-5
  3. 1.4×10-5 -0.567×10-5 = 0.833×10-5
  4. 0.833×10-5 = 8.33×10-6 in scientific notation.
Thus, 1.4×10-5 -5.67×10-6 = 8.33×10-6.

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