# Scientific Notation Addition and Subtraction

How to Add and Subtract Values in Scientific Notation -
Addition and subtraction are one of the basic topics taught to children. However, when we move towards learning harder concepts, operation on values in scientific notations comes into the picture. Let us learn sequentially with the help of examples.
4.5× 10^{4} + 1.7× 10^{5}. Firstly, we need to ensure that both exponents have the same value. Thus, we need to change the value of 1.7 x 105 to 17 x 104. If both already had the same exponential value, you can neglect this step.
4.5× 10^{4}+ 17 × 10^{4}. Now, we will take exponentials common and add the decimal values.
(4.5+ 17) × 10^{4} | 21.5 × 10^{4}. Similar steps are taken for the subtraction phase we just need to retrace our steps and find differences rather than sums.
These lessons and worksheets show you how to perform sums and differences with values that are in scientific notation.

### Aligned Standard: 8.EE.A.4

- Products of Sci. Notation Step-by-Step Lesson- Help the dinosaur jam through this one!
- Guided Lesson - I spent a little more time working on differences here.
- Guided Lesson Explanation - Sometimes it is easier to transfer to standard form first.
- Practice Worksheet - Five products and five differences for you to wrap your head around.
- Matching Worksheet - These matches can actually be determined by the front numbers. Don't get tricked by the powers of ten used.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Get in the habit of writing a parenthesis to help you solve it.

- Homework 1 - The first thing that you want to do is to get all of the powers of ten to the same exponent.
- Homework 2 - Since these are all powers of ten you can easily slide up and down by just moving the decimal point.
- Homework 3 - You can also convert the numbers to standard form when it suits you. You would need to convert it back.

### Practice Worksheets

In my travels, I have found that students have more problem with the differences.

- Practice 1 - Since these are all powers of ten you can easily slide up and down by just moving the decimal point.
- Practice 2 - It all start on the front end and then transitions to the back end.
- Practice 3 - Work on both ends of the problem.

### Math Skill Quizzes

Three to four sum problems followed by six to seven difference problems.

- Quiz 1 - Find the difference of: 7 x 10
^{4}- 1.7 x 10^{2} - Quiz 2 - Find the difference of:
16 x 10
^{2}- 44 x 10^{4} - Quiz 3 - You would need to convert it back.

### When Will You Need to Perform Basic Math Operations with Scientific Notation?

The basic benefit by using scientific forms of values is to be able to quickly communicate humongous or microscopic numbers. Using this form of number notation really makes it easy to write accurate values. There is also another added benefit. When you wish to perform addition or subtraction, it helps make it much faster. This form of notation is sometimes referred to as floating-point because it is based on the base ten system where everything differs by a power of ten. The exponential value expresses the position of decimal point and how many zeros with appear before or after the whole decimal value. Keeping track of that exponential value can prove to be a bit tricky, but if you organize yourself well, it is not bad at all. The more you space out your problems and rewrite them, the easier it will be for you. Take a look at this problem: (2.5 x 10^{3}) + (4.25 x 10^{5}). Right away you notice that the powers of ten differ and will run into difficult. You can restate the problem using the exponent property. The exponent property tells us that b^{m} x b^{n} = b^{(m + n)} Using this well-known property, we can start the problem by rewriting it as:

(2.5 x 10^{3}) + (4.25 x 10^{2} x 10^{3})

Since we have now established a common exponent, we can work the problem further. It would also help us to organize it with a bracket. We can write this as:

(2.5 x 10^{3}) + [(4.25 x 10^{2}) x 10^{3}]

(2.5 x 10^{3}) + (425 x 10^{3})

Now that we have everything in the same format, we can just continue on with solving our operations.

(2.5 + 425) x 10^{3}

(427.5) x 10^{3}

We can then restate this value in proper scientific notation:

(427.5) x 10^{3} = (4.275 x 10^{2}) x 10^{3}

4.275 x 10^{5}

We demonstrated the addition operation, but subtraction is done in much the same way. Like we said before, it is of the utmost importance that you continual space things out and write as much as possible. Restate the problem every step along the way and it will be easy to track.