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How do you multiply #(2.34 xx 10^-8) (5.7 xx 10^-4)#?

Answer 1

Hazel Anglin

See a solution process below:

First, rewrite the expression as:

#(2.34 xx 5.7)(10^-8 xx 10^-4) =>#

#13.338 xx (10^-8 xx 10^-4)#

Next, use this rule for exponents to multiply the 10s terms:

#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#13.338 xx (10^color(red)(-8) xx 10^color(blue)(-4)) =>#

#13.338 xx 10^(color(red)(-8)+color(blue)(-4)) =>#

#13.338 xx 10^-12#

Now, to put this in scientific notation we need to move the decimal point 1 place to the left so we need to add #color(red)(1)# to the exponent of the 10s term:

#1.3338 xx 10^(-12+color(red)(1)) =>#

#1.3338 xx 10^-11#

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Answer 2

Jace Anderson

To multiply numbers in scientific notation, multiply the coefficients (2.34 and 5.7) and add the exponents of 10. So, (2.34 × 5.7) × 10^(−8 + (−4)).

Calculate the coefficients: 2.34 × 5.7 = 13.338. Add the exponents of 10: -8 + (-4) = -12.

Combine the coefficient and the exponent of 10: 13.338 × 10^(-12).

Therefore, the result is 13.338 × 10^(-12).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.