How To Multiply Scientific Notation With Examples

Let’s say our problem is (2×104)×(6×107){\displaystyle (2\times 10^{4})\times (6\times 10^{7})} Our first step would be to multiply the coefficients: 2×6=12{\displaystyle 2\times 6=12}

To continue our example from above, multiplying the bases would look like this: 104×107{\displaystyle 10^{4}\times 10^{7}} Using the rule of exponents, we would convert the problem to 104+107=1011{\displaystyle 10^{4}+10^{7}=10^{11}}, because 4+7=11{\displaystyle 4+7=11}

In our example above, our answer would be 12×1011{\displaystyle 12\times 10^{11}}

(2. 3×104)×(6. 6×107){\displaystyle (2. 3\times 10^{4})\times (6. 6\times 10^{7})} (2. 3×6. 6=16. 38)×(104×107){\displaystyle (2. 3\times 6. 6=16. 38)\times (10^{4}\times 10^{7})} 16. 38×1011{\displaystyle 16. 38\times 10^{11}} Since your coefficient is not in scientific notation (because it’s greater than 10), move the decimal point to the left and convert the problem to scientific notation: 1. 638×101{\displaystyle 1. 638\times 10^{1}} Now, multiply that base by the base we solved for earlier: 101×1011{\displaystyle 10^{1}\times 10^{11}} The answer is 1. 638×1012{\displaystyle 1. 638\times 10^{12}}