Step 1: Make sure both exponents are the same. It’s usually easier to go with the larger exponent so you don’t have to change the exponent in your answer, so let’s make both exponents 6 for this problem. 3.72 x 105 .372 x 106 Step 2: Add the coefficients just as you would regular decimals. Remember to line up the decimals. 1.35 + .372 1.722 Step 3: your answer including the exponent, which is the same as what you started with. 1.722 x 106 Part : Multiplying and Dividing Numbers in Scientific Notation To multiply exponents, multiply the coefficients just as you would regular decimals. Then add the exponents to each other. The exponents DO NOT have to be the same. Example: 1.35 x 106 X 3.72 x 105 = ? Step 1: Multiply the coefficients. 1.35 x 3.72 270 9450 50220 5.022 Step 2: Add the exponents. 5 + 6 = 11 Step 3: Write your final answer. 5.022 x 1011 To divide exponents, divide the coefficients just as you would regular decimals, then subtract the exponents. In some cases, you may end up with a negative exponent. Example: 5.635 x 103 / 2.45 x 106 = ? Step 1: Divide the coefficients. 5.635 / 3.45 = 2.3 Step 2: Subtract the exponents. 3 – 6 = -3 Step 3: Write your final answer. 2.3 x 10-3 Practice: Remember to show all your work, include units if given, and NO CALCULATORS! All work and answers go on your answer sheet. Write the following numbers in scientific notation: 145,000,000,000 13 million 435 billion .000348 135 trillion 24 thousand Complete the following calculations: 3 x 103 + 4 x 103 4.67 x 104 + 323 x 103 7.89 x 10-6 + 2.35 x 10-8 9.85 x 104 – 6.35 x 104 2.9 x 1011 – 3.7 x 1013 1.278 x 10-13 – 1.021 x 10-10 three hundred thousand plus forty-seven thousand 13 million minus 11 thousand 1.32 x 108 X 2.34 x 104
3.78 x 103 X 2.9 x 102 three million times eighteen thousand one thousandth of seven thousand -thousandths of thirty-five million 3.45 x 109 / 2.6 x 103 1.98 x 10-4 / 1.72 x 10-6 twelve thousand divided by four thousand
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