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ISTEP+ Grade 8 - Math: Test Prep & Practice16 chapters | 115 lessons | 4 flashcard sets

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.

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.

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.

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.

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.

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.

To enter scientific notation in a spreadsheet cell we simply enter the number followed by the letter *e* and then the exponent on the 10. For example, if we want to enter 4.4 × 103, we would enter 4.4e3. After pressing the *Enter* key the spreadsheet will be rewritten as *4.4E3+03*. The *E+03* means the initial value is multiplied by 103 giving us 4400.

**Scientific notation** is way to rewrite very large or very small numbers. The exponent on the 10 tells us which way to move the decimal place and how many spaces.

- Positive exponents mean the number is larger than 1 and the decimal place moves to the right.
- Negative exponents mean the number is less than 1 and the decimal places moves to the left.

Scientific and graphing calculators have key such as *EE*, *EXP* or *×10x*, which serve to enter the × 10 to whatever power. The calculator will report answers in scientific notation as a number followed by *E* followed by a number. The number after the *E* is the exponent on the 10.

Spreadsheet programs will represent values in scientific notation with a number followed by an *E*, a positive or negative sign and end with a number. Everything after the *E* is the exponent on the 10.

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ISTEP+ Grade 8 - Math: Test Prep & Practice16 chapters | 115 lessons | 4 flashcard sets

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