# Scientific Notation: Lesson for Kids

Instructor: Michelle Vannoy
In this lesson, we will learn about scientific notation as well as why and how we use it. We will also develop an understanding of what it means to have a positive or negative exponent in scientific notation.

## What Is Scientific Notation?

Did you know that the distance from Earth to the sun is 92,955,807 miles? That's a big number! An even bigger number is the distance from Earth to Pluto: 4,670,000,000 miles. That's a lot of zeroes. Scientists deal with really small numbers, too. For example, the diameter of a hydrogen atom is 0.00000001 centimeters.

Very big and very small numbers can be a pain to deal with. Who wants to write out all of those zeroes every time they have to write a really big or really small number? That's why we have scientific notation, a method of writing very large or very small numbers with a decimal multiplied by a power of 10. For example we would write 4,670,000,000 in scientific notation as 4.67 x 10^9.

## The Parts of Scientific Notation

There are three basic parts of a number written in scientific notation:

• The coefficient is the number that is written before the 'x 10' and tells us what number is being multiplied by a power of 10. The coefficient must always be a number from 1 to 10.
• The base in scientific notation is always 10, since we always multiply by a power of 10 in scientific notation.
• The exponent is the superscript (the smaller number written to the upper-right of the base) that tells us how many times the decimal was moved to make the coefficient a number from 1 to 10.

#### Negative and Positive Exponents

Sometimes, you will see a negative sign before the exponent. Negative exponents mean that the decimal had to be moved to the right to make the original number greater than one so that it followed the rules--so that the coefficient was a number from 1 to 10. So, a number in scientific notation that has a negative exponent is always a number less than 1 in standard notation.

Numbers in scientific notation with a positive exponent are numbers that, in standard notation, are always greater than 1. A positive exponent means the decimal had to be moved to the left to make the original number less than 10.

This is important to keep in mind when converting scientific notation to standard notation, as it tells you which way to move the decimal.

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