Question

Multiply. Write your answer in scientific notation.

Answer 1

Answer:

  1.462 × 10^20

Step-by-step explanation:

Multiplication proceeds in the usual way. The rules of exponents apply. A final exponent adjustment is needed to put the number in scientific notation form. (Your calculator can do all of this for you.)

  (4.3×10^12)(3.4×10^7) = (4.3×3.4)×(10^12×10^7) = 14.62×10^(12+7)

  = 14.62×10^19

  = (1.462×10)×10^19 = 1.462×10^(1+19)

  = 1.462×10^20

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The rule of exponents used is ...

  (a^b)(a^c) = a^(b+c)

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I find it works well to estimate whether the product of the mantissas will be more than 10, then make adjustments to exponents before the multiplication:

  (4.3×10^12)(3.4×10^7) = (4.3×10^12)(0.34×10^8) = 1.462×10^(12+8)

  = 1.462×10^20