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To add or subtract numbers in scientific notation,the bases MUST match. If the bases already match, just add or subtract the coefficients to the same base. 3 x 103 + 4 x 103 = (3 + 4) x 103 = 7 x 103 Bases - they must match in addition or subtraction. Adjust 2 x 103 to .2 x 104. Remember: When one partof the number is adjusted to make the number larger(as in 103 becoming 104, the other part must be adjusted the other way. Add coefficients of the samebase.0.2 x 104 + 4 x 104 = x 104 If adding or subtracting & the bases do not match, first adjust the bases of all numbers to match the larger base. This lines up the decimals. 2 x 103 + 4 x 104 bases Make sure the final answer is in scientific notation. 0.3 x 104 + 2 x 104 = 2.3 x 104 In order to add 3 x 103 + 2 x 104, adjust3 x 103 by making the exponent larger and the 3 smaller by one place value each. 3 x 103 becomes 0.3 x 10 +0.34 x 105 5.2 x 105 + 3.4 x 104 5.2 x 105 x 105 +0.72 x 106 9.2 x 106 + 7.2 x 105 9.2 x 106 x 106 10.52 x 106 +0.72 x 106 9.8 x 106 + 7.2 x 105 9.8 x 106 x 107 Adjust answer to scientific notation. 8.3 x 106 + 3 x 104 x 10 8.3 x 106 - 3 x 104 x 10 9.8 x 106 - 7.2 x 105 x 106 9.8 x 106 - 9.2 x 106 x 105 8.5 x 106 - 5 x 104 x 10 7 x 106 - 5.2 x 104 x 10 7 x 106 + 5.2 x 104 x 10 Commutative Property allows us to move numbers aroundwhen a problem is all multiplication. So change as follows:(2 x 4) • 10(3+4). Make sure the final answer is inscientific notation. If multiplying, decimals DO NOT need to line up;therefore, multiply coefficients. Remember whenmultiplying like based exponents, add the exponents. 2 x 103 • 4 x 104 = x 107 2 x 103 • 4 x 104 2 x 10 • 4 x 10 = 8 x 10 2 6 6 x 10 • 4 x 10 = Remember: Your final answer MUST be in scientific notation. x 10 2 6 3.2 x 10 • 4 x 10 = Remember: Your final answer MUST be in scientific notation. x 10 7 -2 9.5 x 10 • 6 x 10 = Remember: Your final answer MUST be in scientific notation. x 10 -3 6 2.4 x 10 • 4.8 x 10 = Remember: Your final answer MUST be in scientific notation. x 10 5 -2 2.4 x 10 • 4.8 x 10 = Remember: Your final answer MUST be in scientific notation. x 10 -5 -2 Change as follows:(4 ÷ 2) • 10(7-4). Make sure the final answer is inscientific notation. If dividing, decimals DO NOT need to line up;therefore, divide coefficients. Remember whendividing like based exponents, subtract the exponents. 4 x 107 ÷ 2 x 104 = x 103 4 x 107 ÷ 2 x 104 Change as follows:(2 ÷ 4) • 10(7-4) Make sure the final answer is in scientific notation. If dividing, decimals DO NOT need to line up;therefore, divide coefficients. Remember whendividing like based exponents, subtract the exponents. 2 x 107 ÷ 4 x 104 = x 102 2 x 107 ÷ 4 x 104 = .5 x 103 4.8 x 10 ÷ 2.4 x 10 = Remember: Your final answer MUST be in scientific notation. x 10 5 2 2.4 x 10 ÷ 4.8 x 10 = Remember: Your final answer MUST be in scientific notation. x 10 -5 -2 4.8 x 10 • 2.4 x 10 = Remember: Your final answer MUST be in scientific notation. x 10 5 -2 Division may also look like this. 4.8 x 10 2.4 x 10
Remember: Your final answer MUST be in scientific notation. x 10 -2 -5 3.2 x 10 6.4 x 10
Remember: Your final answer MUST be in scientific notation. x 10 3 -4 6.4 x 10 3.2 x 10
Remember: Your final answer MUST be in scientific notation. x 10 3 -4 |