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 = ?
- 8 - 5 = 3. The smaller exponent must be increased by 3.
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2.456×105 = 0.002456×108
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0.002456×108 +6.0034×108 = 6.005856×108
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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 = ?
- 3 - (-2) = 5. The smaller exponent must be increased by 5.
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6.1×10-2 = 0.000061×103
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5.10802×103 -0.000061×103 = 5.107959×103
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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 = ?
- 18 - 12 = 6. The smaller exponent must be increased by 6.
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5.3×1012 = 0.0000053×1018
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3.5×1018 + 0.0000053×1018 = 3.5000053×1018
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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 = ?
- 7 - 3 = 4. The smaller exponent must be increased by 4.
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4.801×103 = 0.0004801×107
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0.0004801×107 -2.2×107 = - 2.1995199×107
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-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 = ?
- -5 - (-6) = 1. The smaller exponent must be increased by 1.
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5.67×10-6 = 0.567×10-5
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1.4×10-5 -0.567×10-5 = 0.833×10-5
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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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