Scientific Notation Quiz

At an elevation of 1221.4 feet, Lake Mead will hold 28,945,000 acre-feet of water. Which number is the best estimate of this amount of water?

The distance from Earth to the Sun is approximately 9 × 10^7 miles. The distance from Earth to the moon is approximately 2 × 10^5 miles. Approximately how many times the distance from the Earth to the Moon is the distance from Earth to the Sun?

• 18

• 45

• 222

• 450

Answer explanation

To find how many times the distance from Earth to the Moon fits into the distance from Earth to the Sun, divide 9 × 10^7 by 2 × 10^5. This gives approximately 45, making the correct answer 45.

A small paper clip weighs about 0.0005 kilogram. What is 0.0005 written in scientific notation?

Answer explanation

To convert 0.0005 to scientific notation, we express it as 5.0 multiplied by 10 raised to the power of -4. Thus, 0.0005 is written as 5 \times 10^{-4}, making this the correct choice.

The average distance from Earth to the Moon is approximately 238,855 miles. Which expression is the best estimate of this distance?

• 2 × 10⁵ miles

• 3 × 10⁵ miles

• 2 × 10⁶ miles

• 3 × 10⁶miles

Answer explanation

The average distance to the Moon is about 238,855 miles. The best estimate in scientific notation is 3 × 10^5 miles, as it rounds to 300,000 miles, which is closest to the actual distance compared to the other options.

• 5.8 × 10⁴ tons

• 4.72 × 10⁴ tons

• 1.66 × 10⁴ tons

• 1.246 × 10⁴ tons

Answer explanation

To find the total weight of the ship with cargo, fuel, and crew, add the empty weight (1.2 × 10^4 tons) to the total weight of cargo, fuel, and crew (4.6 × 10^3 tons). This gives 1.66 × 10^4 tons, which is the correct answer.

• 0.0032

• 0.032

• 320

• 3200

Answer explanation

To convert $3.2 \times 10^{-2}$ to decimal, move the decimal point 2 places to the left, resulting in 0.032. Thus, the equivalent number is 0.032.

The Sun’s mass is about 333,000 times the Earth’s mass. What is 333,000 expressed in scientific notation?

Answer explanation

To express 333,000 in scientific notation, we write it as 3.33 multiplied by 10 raised to the power of 5, since 333,000 = 3.33 x 100,000. Thus, the correct choice is 3.33 \times 10^5.

• 300

• 30,000,000,000

Answer explanation

The speed of light is approximately 3 × 10^{10} cm/s. This is equivalent to 30,000,000,000 cm/s, as 3 × 10^{10} equals 30 billion. Thus, the correct choice is 30,000,000,000.

Guillermo measured a microbe to be 0.0000067 meters across. What is 0.0000067 written in scientific notation?

Answer explanation

To convert 0.0000067 to scientific notation, we express it as 6.7 multiplied by 10 raised to the power of -6. Thus, the correct answer is 6.7 × 10^{-6}.

• 0.00000000873

• 0.0000000873

• 0.000000873

• 0.00000873

Answer explanation

To convert scientific notation to standard form, move the decimal point 8 places to the left. This gives 0.00000000873, which matches the first answer choice.