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In this lesson, we will learn how to express measurements in scientific notation to determine the orders of magnitude of values found from calculations.

Q1:

1 0 J of energy are required to break one DNA strand. How many DNA molecules could be broken by the energy carried by a single electron in the beam of an old-fashioned TV tube that carries 4 × 1 0 J of energy?

Q2:

Determine how many floating-point operations a supercomputer can perform in a human lifetime. Use a value of 1 0 − 1 7 s as the time for a single floating-point operation in a supercomputer and a value of 1 0 9 s for a human lifetime.

Q3:

To the nearest order of magnitude, how many human generations have existed between the year 0 AD and the year 2000 AD? Use a value of 1 0 9 s for an average human lifetime and assume that a generation is one-third of a lifetime.

Q4:

Determine how many floating-point operations a supercomputer can do in one day. Use a value of 1 0 − 1 7 s for the time required for the supercomputer to perform a floating-point operation and use a value of 1 0 5 s for the duration of a day.

Q5:

Determine how many hydrogen atoms placed end to end in a line would stretch across the diameter of the Sun. Use a value of 1 0 − 1 0 m for the diameter of a hydrogen atom and use a value of 1 0 9 m for the diameter of the Sun.

Q6:

A cuboid box has sides of lengths 0.40 mm, 0.30 mm, and 0.20 mm. How many such boxes filled to their brims with water would be required to fill a 1.0-liter-volume container?

Q7:

The total mass of the atmosphere of Mars is 2 . 5 × 1 0 1 6 kg. What is the order of magnitude of this mass?

Q8:

The thickness of the membranes in the cells of living organisms is approximately 1 0 − 8 m. A hydrogen atom has a diameter of roughly 1 0 − 1 0 m. Approximately how many atoms thick is a cell membrane, assuming all atoms within it average about twice the size of a hydrogen atom?

Q9:

Calculate the number of atoms in a bacterium. Assume that the average mass of an atom in the bacterium is 10 times the mass of a proton, that the mass of a proton is 1 0 − 2 7 kg, and that the mass of a bacterium is 1 0 − 1 5 kg.

Q10:

A ping-pong ball has a radius of 40 mm. Calculate the number of ping-pong balls required to fill a cuboid swimming pool of 54.9-meter-length, 27.4-meter-width, and 5.5-meter-depth. Assume a packing density for the ping-pong balls of 0.74 and assume that the balls are not compressed.

Q11:

The semimajor axis distance from Earth to Mars is 2 . 3 × 1 0 1 1 m. What is the order of magnitude of this distance?

Q12:

The mass of Jupiter is 1 . 9 × 1 0 2 7 kg. What is the order of magnitude of this mass?

Q13:

Calculate the approximate number of grains of sand in a layer 10 m deep covering the entire surface of the planet earth. Use a value of 6 3 7 1 km for the radius of the Earth.

Q14:

The deepest point in the world’s oceans can be found in the Mariana Trench in the Pacific Ocean. The maximum known depth is approximately 11 km. The diameter of Earth is roughly 1 0 4 km. Approximately what fraction of Earth’s diameter is the greatest ocean depth?

Q15:

Mount Everest in the Himalayas is the highest mountain on Earth above sea level. The mountain is approximately 9 km tall. The diameter of Earth is roughly 1 0 km. Approximately what fraction of Earth’s diameter is the height of Everest?

Q16:

Determine how many protons are contained in a bacterium. Use a value of 1 0 − 2 7 kg for the mass of a proton and 1 0 − 1 5 kg for that of a bacterium.

Q17:

Assuming one nerve impulse must end before another can begin, what is the maximum firing rate of a nerve in impulses per second?

The duration of a nerve impulse is 1 0 − 3 s.

Q18:

The mass of an alpha-particle is 6 . 6 4 × 1 0 − 2 7 kg. What is the order of magnitude of this mass?

Q19:

The table shows the strengths of the four fundamental forces relative to the strong nuclear force.

What is the strength of the weak nuclear force relative to the strong nuclear force?

What is the strength of the weak nuclear force relative to the electromagnetic force?

What is the strength of the gravitational force relative to the strong nuclear force?

What is the strength of the gravitational force relative to the weak nuclear force?

What is the strength of the gravitational force relative to the electromagnetic force?

Q20:

How many times longer than the mean lifetime of an extremely unstable atomic nucleus is the lifetime of a rabbit? Use a value of 1 0 − 2 2 s for the mean lifetime of extremely unstable atomic nucleus and use a value of 1 0 8 s for the lifetime of a rabbit.

Q21:

A stroboscope is set to flash every 8 . 0 0 × 1 0 − 5 s. What is the frequency of the flashes?

Q22:

The equatorial radius of Mars is 3 . 4 × 1 0 6 m. What is the order of magnitude of this length?

Q23:

The mass of Mars is 6 . 4 × 1 0 2 3 kg. What is the order of magnitude of this mass?

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