Scientific Notation Generated by Technology: Analysis & Examples

Instructor: Matthew Bergstresser
Scientific notation is a way to deal with very large or small numbers. In this lesson, we will go through how to enter scientific notation into various computer-based technology, and how to interpret scientific notation values generated by technology.

Too Large or Too Small

Can you imagine having to do math problems with twenty or thirty digits in a value? Don't just think these are huge numbers. Sometimes these values may be extremely small with twenty decimal places! It might take all day to work calculations with numbers such as these! Luckily we have various forms of technology that can help us deal with these numbers such as scientific or graphing calculators, and computer-based spreadsheet programs. Let's look at how we can use this technology to do the hard work for us when dealing with numbers in scientific notation.

Scientific Notation

Before we deal with entering values in scientific notation in calculator and spread sheets, let's review what scientific notation is. Scientific notation is way to rewrite very large or very small numbers. For example, 602 000 000 000 can be written as 6.02 x 1011. We moved the decimal place, which is after the last zero, to right to be located after the first non-zero number. In this case it is right after the 6. The exponent on the 10 tells us how many spaces we moved the decimal point.

Values larger than 1 get an positive exponent on the 10. Values smaller than 1 get a negative exponent on the 10. For example, the value 0.0000523 can be rewritten 5.23 x 10-5. Now that we have a handle of scientific notation, let's see how to enter these values into calculators and spread sheets.

Graphing and Scientific Calculators

There are a few ways scientific notation can be entered into a calculator. You have to look for one of the following keys on the calculator

• EXP
• EE
• x10x

On some calculators you have to press the shift key or 2nd key to get the scientific notation operation. Let's practice using this function of these calculators to work a problem involving scientific notation.

Example 1

Prompt: What is 4.5 x 1015 × 22?

Solution: Entering this in the graphing and scientific calculator gives us the output 9.9E16 or 9.916. The 16 looks like an exponent on the 9.9, but calculators don't report value answers with exponents so it must represent the exponent on the 10 because it is in scientific notation. This tells us the value is 99 with 15 zeros after it. Since we moved the decimal place one space to the right to get 99, we have 15 spaces to go to represent the answer. Let's work another example.

Example 2

Prompt: Calculate 2.3 x 10-15 divided by 1 x 1015.

Solution: After entering the values into the calculator we get 2.3E-30 or 2.3-30. This means our decimal point needs to move 30 spaces to the left, which is a very small number! Now let's look at how scientific notation is represented in spreadsheet programs on computers.

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