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How do you write and simplify #(7.77 times 10^3 kg)(9.76 times 10^9 m)# in scientific notation?

Answer 1

Jameson Allen

To write and simplify ( (7.77 \times 10^3 , \text{kg})(9.76 \times 10^9 , \text{m}) ) in scientific notation:

Multiply the coefficients: ( 7.77 \times 9.76 = 75.9972 ).
Add the exponents: ( 10^3 \times 10^9 = 10^{3+9} = 10^{12} ).
Combine the coefficient and the exponent: ( 75.9972 \times 10^{12} ).
Round the coefficient to the appropriate significant figures: ( 76.0 \times 10^{12} ).

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Answer 2

Genesis Allen

See the entire solution process below:

First, reword the sentence as follows:

#(7.77 xx 9.76)(10^3 xx 10^9)kg# #m#

Next, increase the terms enclosed in parenthesis:

#75.8352 xx 10^(3 + 9) kg# #m = 75.8352 xx 10^12 kg# #m#

#7.58352 xx 10^13 kg# #m#

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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.