Science: Scientific Notation and Order of Magnitude Estimation Worksheet

Question 1

A wavelength of blue light is about 0.00000042 meters. Write this length in scientific notation.

Accepted Answer

The wavelength is 4.2 x 10^-7 meters. The decimal point moves 7 places to the right, so the exponent is -7.

Question 2

Avogadro's number is about 6.02 x 10^23 particles per mole. Write this number in standard notation using digits.

Accepted Answer

The number is 602,000,000,000,000,000,000,000 particles per mole. The exponent 23 means the decimal point moves 23 places to the right.

Question 3

Sunlight takes about 500 seconds to reach Earth. If light travels at 3.0 x 10^8 meters per second, estimate the distance from the Sun to Earth.

Accepted Answer

The distance is about 1.5 x 10^11 meters. This comes from (3.0 x 10^8 meters per second)(5.0 x 10^2 seconds) = 15 x 10^10 meters = 1.5 x 10^11 meters.

Question 4

A proton has a mass of about 1.67 x 10^-27 kilograms. An electron has a mass of about 9.11 x 10^-31 kilograms. About how many times more massive is a proton than an electron?

Accepted Answer

A proton is about 1.8 x 10^3 times more massive than an electron. Dividing 1.67 x 10^-27 by 9.11 x 10^-31 gives about 0.183 x 10^4, which equals 1.83 x 10^3.

Question 5

A force is measured as 7.8 x 10^5 newtons. To the nearest power of ten, what is its order of magnitude?

Accepted Answer

The order of magnitude is 10^6 newtons. Since 7.8 x 10^5 is closer to 10 x 10^5 than to 1 x 10^5, it rounds to 1 x 10^6.

Question 6

Compare 2.5 x 10^-4 grams and 8.0 x 10^-5 grams. Which mass is larger, and by what factor?

Accepted Answer

The mass 2.5 x 10^-4 grams is larger. The factor is (2.5 x 10^-4) divided by (8.0 x 10^-5) = 3.125, so it is about 3.1 times larger.

Question 7

A classroom shelf has 40 textbooks, and each textbook has about 300 pages. Estimate the total number of pages in scientific notation and give its order of magnitude.

Accepted Answer

The shelf has about 1.2 x 10^4 pages. Its order of magnitude is 10^4 pages.

Question 8

A molecule is about 1.3 x 10^-9 meters wide. Since 1 nanometer equals 1 x 10^-9 meters, write the molecule's width in nanometers.

Accepted Answer

The molecule is about 1.3 nanometers wide. The factor 10^-9 meters is exactly one nanometer, so 1.3 x 10^-9 meters equals 1.3 nanometers.

Question 9

A robot travels 4.2 x 10^6 meters, then travels another 7.5 x 10^5 meters. What total distance did it travel in scientific notation?

Accepted Answer

The robot traveled 4.95 x 10^6 meters. First rewrite 7.5 x 10^5 as 0.75 x 10^6, then add 4.2 x 10^6 + 0.75 x 10^6 = 4.95 x 10^6 meters.

Question 10

A red blood cell is about 8 x 10^-6 meters across, and a virus is about 1 x 10^-7 meters across. About how many times wider is the red blood cell than the virus?

Accepted Answer

The red blood cell is about 80 times wider than the virus. Dividing 8 x 10^-6 by 1 x 10^-7 gives 8 x 10^1, which equals 80.

Question 11

The mass of a small asteroid is estimated to be 3 x 10^12 kilograms. The mass of a spacecraft is about 2 x 10^5 kilograms. About how many times more massive is the asteroid than the spacecraft?

Accepted Answer

The asteroid is about 1.5 x 10^7 times more massive than the spacecraft. This is found by dividing 3 x 10^12 by 2 x 10^5 to get 1.5 x 10^7.

Question 12

Estimate the number of seconds in one year using 365 days per year, 24 hours per day, and 3600 seconds per hour. Write your answer in scientific notation.

Accepted Answer

There are about 3.15 x 10^7 seconds in one year. The calculation is 365 x 24 x 3600 = 31,536,000 seconds, which is 3.1536 x 10^7 seconds.

Question 13

A solution has a concentration of 0.00035 moles per liter. Write the concentration in scientific notation, then give the nearest power of ten.

Accepted Answer

The concentration is 3.5 x 10^-4 moles per liter. The nearest power of ten is 10^-3 moles per liter because 3.5 x 10^-4 is closer to 1 x 10^-3 than to 1 x 10^-4.

Question 14

On a logarithmic scale marked 10^-3, 10^-2, 10^-1, and 10^0, place 5 x 10^-2 in the correct interval and state which power of ten it is closer to.

Accepted Answer

The value 5 x 10^-2 lies between 10^-2 and 10^-1. It is closer to 10^-1 because 5 x 10^-2 equals 0.05, which is closer to 0.1 than to 0.01 on a logarithmic power of ten scale.

Question 15

A small drop of water has a mass of about 0.05 grams. Water has a molar mass of about 18 grams per mole, and 1 mole contains about 6 x 10^23 molecules. Estimate the number of water molecules in the drop.

Accepted Answer

The drop contains about 1.7 x 10^21 water molecules. The number of moles is 0.05 divided by 18, which is about 2.8 x 10^-3 moles, and multiplying by 6 x 10^23 gives about 1.7 x 10^21 molecules.

Science: Scientific Notation and Order of Magnitude Estimation

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