Question

write the following number(s) in scientific notation.
1.) the mass of the earth is 5,973,600,000,000,000,000,000 kg
5.9736×10^24 kg
2.) the human eye blinks an average of 6,500,000 times a year.
6.5×10^6 blinks
3.) the mass of a proton is 0.000000000000000000000167 kg
1.67×10^-27 kg
4.) americans eat 20,000,000,000 hot dogs a year.
2×10^10 hot dogs
5.) the diameter of the human cheek cell ranges in size from 0.00001 m to 0.00005 m.
1×10^-5 m - 5×10^-5 m
write the following numbers in standard notation.
6.) the length of a flea is 5.0×10^-4m.
0.0005 m
7.) the human heart beats an average of 4.2×10^7 times a year.
42000000 beats
8.) there are approximately 2.5×10^10 red blood cells in the human body.
25000000000 cells
9.) the average red blood cell is 7×10^-6 m in diameter.
0.000007 m

Explanation:

Step1: Recall scientific - notation rule

Scientific notation is of the form $a\times10^{n}$, where $1\leq a < 10$ and $n$ is an integer.

Step2: Rewrite Earth's mass

For the mass of the Earth $5973000000000000000000$ kg, move the decimal point 21 places to the left. So it is $5.973\times 10^{21}$ kg.

Step3: Rewrite proton's mass

For the mass of a proton $0.000000000000000000000167$ kg, move the decimal point 27 places to the right. So it is $1.67\times 10^{-27}$ kg.

Step4: Rewrite hot - dog consumption

For Americans eating $20000000000$ hot - dogs a year, move the decimal point 10 places to the left. So it is $2\times 10^{10}$ hot - dogs.

Step5: Rewrite cheek - cell diameter

For the diameter of the human cheek cell from $0.00001$ m to $0.00005$ m, $0.00001 = 1\times 10^{-5}$ m and $0.00005=5\times 10^{-5}$ m.

Step6: Recall standard - notation rule

To convert from scientific notation $a\times 10^{n}$ to standard notation, if $n>0$, move the decimal point $n$ places to the right; if $n < 0$, move the decimal point $|n|$ places to the left.

Step7: Convert flea length

For the length of a flea $5.0\times 10^{-4}$ m, move the decimal point 4 places to the left. So it is $0.0005$ m.

Step8: Convert heart - beat count

For the human heart beats $4.2\times 10^{7}$ times a year, move the decimal point 7 places to the right. So it is $42000000$ beats.

Step9: Convert red - blood - cell count

For the number of red blood cells $2.5\times 10^{10}$ in the human body, move the decimal point 10 places to the right. So it is $25000000000$ cells.

Step10: Convert red - blood - cell diameter

For the average red blood cell diameter $7\times 10^{-6}$ m, move the decimal point 6 places to the left. So it is $0.000007$ m.

Answer:

1. $5.973\times 10^{21}$ kg
2. $6.5\times 10^{6}$ blinks
3. $1.67\times 10^{-27}$ kg
4. $2\times 10^{10}$ hot dogs
5. $1\times 10^{-5}$ m to $5\times 10^{-5}$ m
6. $0.0005$ m
7. $42000000$ beats
8. $25000000000$ cells
9. $0.000007$ m