Question #ad67c

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Question #ad67c

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Answer 1 · 2017-10-17T23:28:37

$(2.3 \times 10^{7}) (1.4 \times 10^{- 2}) = 3.2 \times 10^{5}$ $(2.3 xx 10^7)(1.4xx10^-2) = 3.2xx10^5$

Explanation:

Start by looking at the exponents or powers of the two decimal numbers to see that this is a large number (tens of millions) multiplied by a relatively small number (hundredths or 1/100).
So the answer will lay somewhere in the thousands.

$(2.3 \times 10^{7}) (1.4 \times 10^{- 2})$ $(2.3 xx10^7)(1.4 xx10^-2)$

To multiply exponents, we need to add them: $10^{7} + 10^{- 2} = 10^{5}$ $10^7+10^-2=10^5$
but we still must be on the look out for additional powers if the decimal numbers multiply to be above $10.0$ $10.0$ - here they do not.

$(2.3 \times 10^{7}) (1.4 \times 10^{- 2}) = d . d \times 10^{5}$ $(2.3 xx10^7)(1.4xx10^-2)=d.d xx10^5$

and we can solve for: $d . d = 2.3 \times 1.4 = 3.22$ $d.d=2.3xx1.4=3.22$ rounded to $3.2$ $3.2$

So: $(2.3 \times 10^{7}) (1.4 \times 10^{- 2}) = 3.2 \times 10^{5}$ $(2.3 xx10^7)(1.4xx10^-2) = 3.2xx10^5$

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Question #ad67c

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