Question

1. According to the U.S. Energy Information Administration (www.eia.gov) the United States consumed 4.151 trillion kWh (kilowatt-hours) of electric energy in 2010. Write this number in correct scientific notation in terms of kWh. 2. Of this electric energy, 260.2 billion kWh were produced by hydroelectric sources (think water over dams – like Snoqualmie Falls) in 2010. a) Write this number in correct scientific notation in terms of kWh. b) What percent of the total US electric energy did hydroelectric sources account for in 2010? (Round to the nearest 10th of a percent.)

Answer 1

Answer :

For part (1) :

The correct scientific notation in terms of kWh is $2.602\times 10^{11}$

For part (2) :

(a) The correct scientific notation in terms of kWh is $2.602\times 10^{11}$

(b) The percent of the total US electric energy is 6.27 %

Explanation :

Scientific notation : It is the representation of expressing the numbers that are too big or too small and are represented in the decimal form with one digit before the decimal point times 10 raise to the power.

For example :

5000 is written as $5.0\times 10^3$

889.9 is written as $8.899\times 10^{-2}$

In this examples, 5000 and 889.9 are written in the standard notation and $5.0\times 10^3$  and $8.899\times 10^{-2}$  are written in the scientific notation.

If the decimal is shifting to right side, the power of 10 is negative and if the decimal is shifting to left side, the power of 10 is positive.

For part 1 :

As we are given the energy 4.151 trillion kWh in standard notation.

Trillion means $10^{12}$

Now converting this into scientific notation, we get:

$\Rightarrow 4.151 \text{trillion}=4.151\times 10^{12}$

Hence, the correct scientific notation in terms of kWh is $4.151\times 10^{12}$

For part 2 :

(a) As we are given the energy 260.2 billion kWh in standard notation.

Billion means $10^{9}$

Now converting this into scientific notation, we get:

$\Rightarrow 260.2 \text{billion}=260.2\times 10^{9}=2.602\times 10^{11}$

As, the decimal point is shifting to left side, thus the power of 10 is positive.

Hence, the correct scientific notation in terms of kWh is $2.602\times 10^{11}$

(b) Now we have to calculate the percent of the total US electric energy.

$\text{Percent of total US electric energy}=\frac{2.602\times 10^{11}}{4.151\times 10^{12}}\times 100=6.27\%$

Thus, the percent of the total US electric energy is 6.27 %