# Scientific notation

Do you need a scientific notation calculator? You are in the right place because thanks to our converter, you will be able to express a number in the following notations:

• Decimal notation
• Scientific or exponential notation
• Notation E (symbolizes the exponent)
• Engineering notation

All you have to do is write the number in the corresponding notation and click the convert button to the right of the box to convert to the other notations.

It is important that do not use thousands separator in the number you write and if there are decimals, use the period (.) instead of the comma (,).

## What is scientific notation used for?

Scientific notation is very useful when working with very large or very small numbers. This is done because it is much easier to read a number with an exponent to a figure that accumulates a large number of decimals or zeros, saving also a lot of space when writing it.

For example, do youhow to express the distance from the earth to the sun in scientific notation? Scientists have established that between the sun and our planet there are 149,597,870,700 meters.

As you can see, this is a figure that is too large and difficult to remember. use scientific notation for it and we are left with the distance from the earth to the sun in scientific notation as 1.49 x 1011 meters. Much more comfortable, isn't it?

Now that you know what scientific notation is forLet's see how a number is expressed in this form.

## How to write a number in scientific notation

Now that we know what the exponential notationLet's see how to express a number in this way. First of all, it is important to know that a number in scientific notation looks like this

m x 10e

Being:

• m is the mantissa and its value must be greater than or equal to 1 or less than 10.
• e is the number that represents the exponent and determines the order of magnitude

Depending on whether the number we want to convert to exponential notation is positive less than 1, we will have to do it in one way or another. For that reason, we are going to see each case individually so that it is well explained.

### Expressing a positive number in scientific notation If we have a number we want to express in exponential notationyou have to:

• Move the comma as many places to the left as there are to reach the first whole number.
• Write as the exponent number the number of places you have moved the decimal point.

For the sake of clarity, let's look at some of them. step-by-step examples. If we want to pass the number 43242.55 in scientific notation, we will have to:

• Move the decimal point four positions to the left, just before the first integer number
• As we have moved the comma four positions, the exponent will be 4

Therefore, we are left with the number 43242.55 expressed in scientific notation as 4.324255 x 104.

Let's look at another example. If we are given the number 432,234 and we are asked to convert it to scientific notation, we will get 4.32 x 105. Below you can see how we arrived at this result:

432234

43223,4 x 101

4322,34 x 102

432,234 x 103

43,2234 x 104

4,32234 x 105

Easy, isn't it? Let's see now how to act in the case of numbers less than 1.

### Putting a number less than 1 into scientific notation If the number to be represented in scientific notation is less than 1, the procedure to follow is slightly different from what we have seen in the previous point. In this case we will do the following:

• Move the comma to the right as many positions as there are until the first integer is reached
• We will write as the number of negative exponent the number of positions we have moved the comma to the right.

For example, if we are given the number 0.00051 and we want to represent it in scientific notation, we will do it like this:

0,00051

0,0051 x 10-1

0,051 x 10-2

0,51 x 10-3

5,1 x 10-4

Remember the condition that the mantissa must be greater than or equal to 1 and less than 10. This is a good criterion to know where to stop if you are not very clear.

Even so, if you have any questions, leave us a comment and we will help you solve them.

## Scientific notation in Excel If you are going to use Excel and want to express the cell contents in scientific notationyou must do the following steps:

1. Type in the numbers you want in the cells you need
2. Select the cells in which you want the content to be represented in scientific notation.
3. Go to the Format > Cells menu and change the category to "Scientific". If desired, select the number of decimal places with which you want the result.

## Operations with scientific notation

If you work with scientific notation, you are interested in learning how to perform basic operations such as addition, subtraction, multiplication, division, etc.

For the addition or subtraction of two numbers with scientific notationIf they do not have the same exponent, it is essential that both have the same exponent. If they do not have the same exponent, you will have to transform them properly for this condition to be met.

Once both numbers have the same exponent, the addition or subtraction is solved by adding or subtracting the value of the mantissa. The exponents remain the same.

Examples:

4,2 - 107 + 3,5 - 105 = 420 - 105 + 3,5 - 105 = 423,5 - 105 = 4,235 - 107

6,32 - 109 - 6,25 - 109 = 0,07 - 109 = 7 -107

### Multiplication

At the time of multiplying numbers in scientific notationwe have to:

• Multiplying mantises
• Add the value of the exponents

Since the result will probably not be in scientific notation, we will have to adjust it as we have learned.

Example:

(6,5 - 108) - (3,2 - 105) = (6,5 - 3,2) - 108+5 = 20,8 - 1013 = 2,08 - 1014

Division

In the division of numbers in scientific notation we must do the opposite of multiplication, that is:

• Dividing the mantissae
• Subtract the exponents

Again, it is likely that we will have to convert the result obtained in the division to scientific notation.

Example:

(8 - 1017) / (2 - 109) = (8/2) - 1017-9 = 4 - 108

## Engineering notation

Engineering notation is slightly different from scientific notation. In the case of engineering notation, the value of the exponent must always be a multiple of 3.

For example, the number 34 x 106 would be a number expressed in engineering notation.

## Examples of scientific notation Finally, we leave you with several examples of scientific notation for you to practice by yourself.

• 0,00000256 = 2,56×10-6
• 0,00000014 = 1,4×10-7
• 0,000275 = 2,75×10-4
• 1.988.000.000.000.000.000.000.000.000.000 = 1,988 × 1030
• 3,2 =3,2 × 100
• 0,0055 = 5,5 10-3
• 24327 = 2.4327 x 104
• 7354 = 7.354 x 103
• 482 = 4.82 x 102
• 89 = 8.9 x 101

### How many seconds is a year in scientific notation?

To solve this exercise the first thing we have to do is to calculate the number of seconds in a year.

We know that an hour has 3600 seconds, therefore, a day will have:

24 hours x 3600 seconds = 86,400 seconds

As a year has 365 days, we are left with:

365 days x 86,400 seconds = 31,536,000 seconds = 3.1536 x 107

If you want to try with any number, you can make up any number you want and use our scientific notation converter to check if the result you have obtained is correct.

And if you have any questions, leave us a comment and we will help you.