Question

Hi, question. Does anyone know how to solve

(5.4×10^-1)(7×10^0)

Answer 1

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

Answer 2

In scientific notation.

Answer 3

I forgot to mention that detail.

Answer 4

first, multiply the mantissa of one by the mantissa of the other. \[5.4*7 = \]

Answer 5

Okay.

Answer 6

what do you get?

Answer 7

37.8

Answer 8

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:
\[37.8*10^{-1}\]

Answer 9

Okay.

Answer 10

Thank you

Answer 11

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

Answer 12

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.

Answer 13

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?

Answer 14

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

Answer 15

we are essentially converting\[37.8*10^{-1}\]to\[\frac{1}{10}*37.8*10^{-1}*10\]to\[3.78*10^{-1+1} = 3.78*10^0\]

Answer 16

Thank you

Answer 17

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

Answer 18

Right.

Answer 19

Yup! I'd do the same haha

Answer 20

such an answer deserves a medal :-)

Answer 21

Okay. Thanks.