A Complete Explanation of How to do Scientific Notation

A Short Intro on Converting to Scientific Notation

How to Convert to Scientific Notation Quickly

Changing over Numbers to Scientific Notation accurately means that the coefficient must be somewhere in the range of 1 and 10. When figuring out Scientific Notation you should move the decimal point in the first number with the goal that it makes a number that is in the middle of 1 and 10. That number will be the new coefficient. The quantity of spaces that you moved the decimal will be the quantity of the example on the Power of 10. The power will be negative if you move the decimal left. The power will be positive if you move the decimal right.

A short video on our Converting to Scientific Notation Worksheet

Watch our free video on Converting to Scientific Notation. This video shows how to solve problems that are on our free Converting to Scientific Notation worksheet that you can get by submitting your email above.

Watch the free Converting to Scientific Notation video on YouTube here: Converting to Scientific Notation

Video Transcript:

This video is about converting numbers to scientific notation. You can get the scientific notation worksheets for 8th grade used in this video for free by clicking on the link in the description below.

In order to show you how to do scientific notation, you have to first know the main parts of scientific notation. There are two main parts of converting scientific notation, that is the base being multiplied times a power of 10. For example, you could have something like seven point seven times ten to the 8th power. The base always has to be in between 1 and 10 and the power of 10 is always a base of 10 being multiplied times an exponent. In order to show you how to do scientific notation you’re going to be taking really, really large numbers, like say 7 million, and rewriting it into the form of scientific notation, or really, really small numbers. like say point 0 0 0 0 5. And rewriting it into scientific notation.

Now you will notice a few things about our rewritten numbers into scientific notation. Our base here is in between 1 and 10. It did not matter if the number was really large like 7 million or if it was really small like point 0 0 0 0 5. The base remains in between 1 and 10.

In order to get the exponent you have to count how many times you move the decimal to get to a point where the base will be in between 1 and 10. For this number we moved six times so our exponent was 6. For this number we moved it 5 times so our exponent was 5.

Now you will notice that this 6 is positive and this 5 is negative. The easiest way to remember if an exponent will be positive or negative is that to get a positive exponent our starting number is larger than one and then to get a negative exponent your starting number is a decimal or less than one. If you look this number here point zero zero zero zero five is less than one it’s a decimal and our exponent ends up being negative. This number seven million is much larger than one so our exponent is positive.

The first problem on the scientific notation practice worksheet we’re going to do is number one.  Our directions say to convert the following numbers in the scientific notation. We have to convert 500 into negative scientific notation. We know our decimal starts here we have to move the decimal to a spot that will create a base that is in between 1 and 10. In this case if we move the decimal two times, our base will become 5. If you moved it one more time it would become 0.5 that is not in between 1 and 10 so we don’t want to use that. We’ll stop right here 5 then we move the decimal two times. We know that the exponent on the power of 10 will be 2 and this time it’s positive because we started with a number greater than 1. Sorry the solution for 500 in scientific notation is 5 times 10 to the 2nd power.

The next problem we’re going to do is number three. Number three gives us point zero zero seven. The first thing you have to do is we have to take our decimal and we have to move it to a spot that will create a base in between 1 and 10. If we move it to here, it will create a base in between 1 and 10. Now we have to figure out what our exponent is going to be. Well if you look, we move the decimal one two three times so our exponent will be three because we moved it three times. But we started as a decimal which is less than one so point zero zero seven is less than one and because this is a decimal that means our exponent must be negative. Our final answer is 7 times 10 to the negative 30.

The last problem we’re going to do is number six. We are given point zero zero zero zero zero four five. The first thing we must do is we must move the decimal to a spot that will create a base in between 1 and 10, in this case we move it to in between 4 & 5 because 4 point 5 is in between 1 and 10. This is our base and we have to include both the 4 and the 5 because they are both a part of the original number. When you write the base you have to write 4.5 because it’s both a part of the decimal. Then we’re going to write our second part of our scientific notation negative exponent which is times a power of 10 and then we’re going to count how many times we move the decimal. We moved it one two three four five six times  our so our exponent is six but our number starts as a decimal which means that the exponent must be negative because we started with a decimal. And 4.5 times 10 to the negative six is going to be the solution for this. You can try the practice problems by downloading the free writing numbers in scientific notation worksheet above.