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anonymous

  • one year ago

Hi, question. Does anyone know how to solve (5.4×10^-1)(7×10^0)

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  1. whpalmer4
    • one year ago
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    there's no equation there to solve. Do you mean how to multiply it out?

  2. anonymous
    • one year ago
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    In scientific notation.

  3. anonymous
    • one year ago
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    I forgot to mention that detail.

  4. whpalmer4
    • one year ago
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    first, multiply the mantissa of one by the mantissa of the other. \[5.4*7 = \]

  5. anonymous
    • one year ago
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    Okay.

  6. whpalmer4
    • one year ago
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    what do you get?

  7. anonymous
    • one year ago
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    37.8

  8. whpalmer4
    • one year ago
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    good next, we multiply the two exponential parts: \[10^{-1}*10^0\]by adding the exponents:\[10^{-1}*10^{0} = 10^{-1+0} = 10^{-1}\] then we multiply that with the product we got for the mantissa part: \[37.8*10^{-1}\]

  9. anonymous
    • one year ago
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    Okay.

  10. anonymous
    • one year ago
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    Thank you

  11. whpalmer4
    • one year ago
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    Now, the mantissa is always supposed to have an absolute value between 1 and 10 if it isn't, then you need to normalize it

  12. whpalmer4
    • one year ago
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    which means divide or multiply by 10 as many times as needed, and adjust the exponent so that you aren't changing the value of the number.

  13. whpalmer4
    • one year ago
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    here we have 37.8, which is too big, so we divide by 10 to get 3.78, and we adjust the exponent up by 1. does that make sense?

  14. anonymous
    • one year ago
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    Not really. I'll probably have to go in before finals in the morning.

  15. whpalmer4
    • one year ago
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    we are essentially converting\[37.8*10^{-1}\]to\[\frac{1}{10}*37.8*10^{-1}*10\]to\[3.78*10^{-1+1} = 3.78*10^0\]

  16. anonymous
    • one year ago
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    Thank you

  17. whpalmer4
    • one year ago
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    37.8 * 0.1 is the same as 3.78 * 1, right? that's all we did in the normalization step

  18. anonymous
    • one year ago
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    Right.

  19. anonymous
    • one year ago
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    Yup! I'd do the same haha

  20. whpalmer4
    • one year ago
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    such an answer deserves a medal :-)

  21. anonymous
    • one year ago
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    Okay. Thanks.

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