How do you add subtract multiply and divide using scientific notation? - Answers

When dealing with numbers in scientific notation the mantissa (number with the decimal point) and the exponent (the × 10^n bit) are processed separately: To add and subtract: the exponents (powers of 10) MUST be the same: 1) If the exponents are different, adjust the number with the greater power so that the exponents are the same; 2) add/subtract the numbers like normal decimals (with the decimal points aligned), keeping the exponent; 3) Adjust the result back to proper scientific notation if necessary. eg: 1.23 × 10^4 + 2.34 × 10^3 Adjust the 1.23 × 10^4 → 12.3 × 10^3 → 1.23 × 10^4 + 2.34 × 10^3 = 12.3 × 10^3 + 2.34 × 10^3 = (12.3 + 2.34) × 10^3 = 14.64 × 10^3 = 1.464 × 10^4 eg 9.83 × 10^4 + 2.7 × 10^3 = 98.3 × 10^3 + 2.7 × 10^3 = (98.3 + 2.7) × 10^3 = 101 × 10^3 = 1.03 × 10^5 eg 1.05 × 10^4 - 2.7 × 10^3 = 10.5 × 10^3 - 2.7 × 10^3 = (10.5 - 2.7) × 10^3 = 7.8 × 10^3 To multiply and divide: 1) multiply/divide the mantissas; 2) add/subtract the powers in the exponents; 3) Adjust the result back to proper scientific notation if necessary. eg 1.23 × 10^4 × 2.34 × 10^3 = (1.23 × 2.34) × 10^(4 + 3) = 2.8782 × 10^7 eg 9.83 × 10^4 × 2.7 × 10^-3 = (9.83 × 2.7) × 10^(4 + -3) = 26.541 × 10^1 = 2.6541 × 10^2 eg 1.05 × 10^5 ÷ 2.3 × 10^3 = (1.05 ÷ 2.3) × 10^(5 - 3) ≈ 0.4565 × 10^2 = 4.565 × 10^1 eg 1.155 × 10^5 ÷ 2.1 × 10^-3 = (1.155 ÷ 2.1) × 10^(5 - -3) = 0.55 × 10^8 = 5.5 × 10^7