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Find out the product of 5.2 × 10^{3} and 6.5 × 10^{7}. Write your answer in scientific notation.
To multiply numbers written within scienti?c notation, multiply the ?rst numbers (5.2 × 6.5 = 33.8). Then, multiply the powers of ten through adding the exponents (10^{3} × 10^{7} = 10^{10}); 33.8 × 10^{10} is the answer, except it is not in scienti?c notation. The decimal in 33.8 must be moved to form a number among 1 and 10. Placing the decimal among the 3's will accomplish this (3.38). Since the decimal has been moved once to the left, the exponent of ten must be increased through 1. The answer is 3.38 × 10^{11}.
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