# Scientific Notation Worksheets

What is Scientific Notation? There are times when we have to deal with numbers that are too big or too small to write and can take up a lot of our time. It is where we can use scientific notations. These notations are a part of mathematical language, which makes problem-solving simpler and much more convenient.
Scientific notations are a way we can easily write a number that is too big or small as a product of a real number and power of 10. The general form of a number written in scientific notation is;
a × 10^{b}. Here; a is the coefficient and b is the exponent. The co-efficient is a non-zero value and is a combination of an integer, decimal point, and a mantissa. The mantissa is a term that many students are unaware of. It is the digits that lie on the right side of decimal and hold significant value.
Consider the number 0.000000000000162 | When you are writing down this number, there are chances that you miss out one or two zeros on the right side of the decimal and it can expose your calculations to errors. Therefore, you can write it in a simpler manner; 1.62 × 10^{-14}
When you have to move the decimal to the right-hand side of the decimal, the exponent becomes negative, and when the decimal moves towards the left, the exponent becomes positive.
Get started with powers of ten and then work your way towards using this form of notation in our word problems. Did you know that scientists account for 90% of the usage of this form of notation, I guess that was a no brainer!

# Scientific Notation Worksheet Categories

- Powers of Ten and Scientific Notation - We show how these forms of notation are used to represent very large and very small numbers. This can help us communicate these difficult to quantify values very quickly and with ease.
- Scientific Notation Word Problems - These are practical problems that you will find in most High School science lab environments. You will also see this skill come up in many different advanced math programs.
- Scientific Notation Addition and Subtraction - Yes, there are a few tricks to calculating these quickly. Make sure that you have a good handle on the concept of place value and the meaning of a base ten number. That will come in very helpful.
- Scientific Notation Multiplication and Division - This is one of the tougher section for students that are studying this topic. When students work with these values and using product operations, they do not have much trouble. As the kids move up to quotients, in this environment, it can get difficult quickly.

### Where Is Scientific Notation Used in The Real World?

This is a very common question that many students will have. It is important to see value in the things that you learn. It helps motivate you and keep you focused. The first use of scientific notation is not well documented, but it become more and more common place as scientific research grew. In the nineteenth century, it started really to bubble up and work its way to become the scientific standard by the twentieth century. As research begins to explore now layers of the universe and microscopic regions of our world, this form of notation is not only needed, but required in order to communicate the results of experiments as well to explain the movement of such matter. Things in the universe are very large and the distances between them are very far apart. To convey these dimensions with data we have to use immense values. For example, the planet Jupiter is enormous. If you were to combine all the other planets in the Milky Way Galaxy, Jupiter would still be two and half times their mass. This is because Jupiter's mass is 1.9 x 10^{27} kilograms. If we were to remove the notation we would be working with the value as: 1,900,000,000,000,000,000,000,000,000. I added the commas for my own sanity. All known elements are made up of protons, neutrons, and electrons. Protons and neutrons are made up of even tinier building blocks called quarks. A quark is 0.43 x 10^{-16} centimeters in size. That is forty-three billion-billionths of a single centimeter. If we were to remove the scientific notation the value would be: 0.000000000000000043. Simply be using this way to express values, think of all of the paper we are saving the world. Needless to say, if you decide on a career in research, of any kind, you can expect to make it a habit of using scientific notation on a daily basis.