Put Scientific Notation to Work in Physics Problems

By Steven Holzner

Physics deals with some very large and very small numbers. To work with such numbers, you use scientific notation. Scientific notation is expressed as a number between 1 and 10 multiplied by a power of 10.

For example, suppose you’re measuring the mass of an electron in the MKS system. You put an electron on a scale (in practice, electrons are too small to measure on a scale — you have to see how they react to the pull of magnetic or electrostatic forces to measure their mass), and you measure the following:

0.00000000000000000000000000000091 kg

What the heck is that? That’s a lot of zeros, and it makes this number very unwieldy to work with. Fortunately, you know all about scientific notation, so you can convert the number into the following:

9.1 x 10–31 kg

That is, 9.1 multiplied by a power of 10, 10–31. Scientific notation works by extracting the power of 10 and putting it on the side, where it’s handy. You convert a number to scientific notation by counting the number of places you have to move the decimal point to get the first digit in front of that decimal point.

For example, 0.050 is 5.0 x 10–2 because you move the decimal point two places to the right to get 5.0. Similarly, 500 is 5.0 x 102 because you move the decimal point two places to the left to get 5.0.

Sample question

  1. What is 0.000037 in scientific notation?

    The correct answer is 3.7 x 10–5. You have to move the decimal point five times to the right to get 3.7.

Practice questions

  1. What is 0.0043 in scientific notation?

  2. What is 430,000.0 in scientific notation?

  3. What is 0.00000056 in scientific notation?

  4. What is 6,700.0 in scientific notation?

Following are answers to the practice questions:

  1. 4.3 x 10–3

    You have to move the decimal point three places to the right.

  2. 4.3 x 105

    You have to move the decimal point five places to the left.

  3. 5.6 x 10–7

    You have to move the decimal point seven places to the right.

  4. 6.7 x 103

    You have to move the decimal point three places to the left.