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Mathematics I (Math 1132)

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Durham College, Mathematics
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Mathematics I (Math 1132)

Scientific Notation

If you’ve ever tried multiplying numbers in the millions and billions on your calculator,  you’ve either gotten an error or some number that looks like this:

Notice how this calculator condenses the large output with E17. The E17 is the calculators way of writing:

×1017   or   ×100 000 000 000 000 000

On paper, we can also condense very large or tiny outputs using scientific notation. Examples of numbers written in scientific notation look like the following:

Notice how all of them have the same pattern: a number followed by a decimal and more numbers times 10 to the power of a positive or negative integer. The steps to converting any ordinary number to this notation is outlined below:

To convert a decimal number to scientific notation:

  1. Rewrite the given number with a single digit to the left of the decimal point, discarding any non-significant zeros.

273 → 2.73

2. Then multiply this number by the power of 10 that will make it equal to the original number.

2.73 × 100   →   2.73 × 10²

  • Notice how the power of 2 corresponds to the number zeros in 100.

The first video provides a quick tutorial of what’s stated above, including some examples where the number is negative, between -1 and 1, and numbers greater than 1.

There will also be times when you’ll be expected to go from scientific notation to standard, decimal notation. Let’s make sure we know how that’s done too. Here are few examples to follow along to:

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