## 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

there's no equation there to solve. Do you mean how to multiply it out?

2. anonymous

In scientific notation.

3. anonymous

I forgot to mention that detail.

4. whpalmer4

first, multiply the mantissa of one by the mantissa of the other. $5.4*7 =$

5. anonymous

Okay.

6. whpalmer4

what do you get?

7. anonymous

37.8

8. whpalmer4

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

Okay.

10. anonymous

Thank you

11. whpalmer4

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

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

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

Not really. I'll probably have to go in before finals in the morning.

15. whpalmer4

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

Thank you

17. whpalmer4

37.8 * 0.1 is the same as 3.78 * 1, right? that's all we did in the normalization step

18. anonymous

Right.

19. anonymous

Yup! I'd do the same haha

20. whpalmer4

such an answer deserves a medal :-)

21. anonymous

Okay. Thanks.