# Scientific Notation

## Key Questions

• Because accuracy of calculations are very important.

When scientists are working with very large or small numbers, it's easy to lose track of counting the $0$'s!

If I gave you,

$3 \cdot {10}^{-} 10$, or

$0.0000000003$

which would be easier to work with?

• Scientific notation means that you write a numeral as a number multiplied by 10 to a power.

For example, we can write 123 as 1.23 × 10², 12.3 × 10¹, or 123 × 10⁰.

Standard scientific notation puts one nonzero digit before the decimal point. Thus, all three of the above numbers are in scientific notation, but only 1.23 × 10² is in standard notation.

The exponent of 10 is the number of places you must shift the decimal point to get the scientific notation. If you move the decimal place to the left, the exponent is positive. If you move the decimal place to the right, the exponent is negative.

Examples:

'200. = 2.00 × 10²
The decimal moved left 2 places, so we use 2 as the exponent.

0.0010 = 1.0 × 10⁻³
The decimal moved right 3 places, so we use -3 as the exponent.

Problem:

Write the following numbers in standard scientific notation: 1001; 6 926 300 000; -0.0392

Solution:

1.001× 10³; the decimal moved left 3 places, so we use 3 as the exponent.

6.9263 × 10⁹; the decimal moved left 9 places, so we use 9 as the exponent.

-3.92 × 10⁻²; the decimal moved right 2 places, so we use -2 as the exponent.

Here is a video which discusses the topic of scientific notation.

• Scientific notation is used to write numbers which are either very big or very small.

This video discusses how to write numbers in scientific notation.

This video shows how to add numbers written in scientific notation and use rules for sig figs.

This video discusses how to use scientific notation on a TI graphing calculator and avoid a common calculation error.