Converting to Scientific Notation Worksheet, Rules, and Examples

Get the free How to do Scientific Notation worksheet and other resources for teaching & understanding How to do Scientific Notation

How to Write Numbers in Scientific Notation Explained in 4 Simple Steps | 8th Grade

Key Points about Converting to Scientific Notation

  • Scientific notation is a shorthand method that uses powers of ten to represent numbers that are either too large or too small to be easily expressed in standard decimal form.
  • Exponents play a crucial role in scientific notation, representing the number of times that ten is multiplied by itself to arrive at a given value.
  • Scientific notation can be used to represent both small and large numbers, and converting numbers to scientific notation involves moving the decimal point and adjusting the exponent accordingly.

Converting to Scientific Notation

Converting to Scientific Notation involves understand that in order for a number to be written correctly in Scientific Notation the coefficient must be between 1 and 10. When Converting to Scientific Notation you must move the decimal point in the original number so that it creates a number that is in between 1 and 10. That number will be the new coefficient. The number of spaces that you moved the decimal will be the number of the exponent on the power of 10. If you moved the decimal point to the right, the exponent will be negative. If you moved the decimal point to the left, the exponent will be positive.

Scientific notation is a way of expressing numbers that are either too large or too small to be easily written in standard decimal form. It is a shorthand method that uses powers of ten to represent these numbers in a more compact and manageable way. Understanding scientific notation is an essential skill for anyone working in the fields of science, engineering, or mathematics.

The role of exponents in scientific notation cannot be overstated. Exponents are used to represent the number of times that ten is multiplied by itself to arrive at a given value. For example, the number 1,000,000 can be expressed in scientific notation as 1 x 10^6, which means that ten is multiplied by itself six times to arrive at this value. Similarly, the number 0.00001 can be expressed as 1 x 10^-5, which means that ten is divided by itself five times to arrive at this value.

Scientific notation can be used to represent both small and large numbers. For small numbers, the exponent will be negative, while for large numbers, the exponent will be positive. Converting numbers to scientific notation involves moving the decimal point to the left or right until only one digit remains to the left of the decimal point. Operations in scientific notation involve multiplying or dividing the coefficients and adding or subtracting the exponents. Frequently asked questions about scientific notation include how to round numbers in scientific notation, how to compare numbers in scientific notation, and how to convert scientific notation to standard decimal form.

Common Core Standard: 8.EE.A.3
Related Topics: Square Roots, Cube Roots, Irrational Numbers, Powers of 10, Scientific Notation Intro, Converting Numbers from Scientific Notation, Adding and Subtracting in Scientific Notation, Multiplying in Scientific Notation, Dividing in Scientific Notation
Return To: Home, 8th Grade

How to do Scientific Notation

Understanding Scientific Notation

Scientific notation is a way of representing very large or very small numbers in a more concise and manageable format. It is commonly used in scientific and mathematical calculations, where large or small numbers can be difficult to work with. In scientific notation, a number is expressed as a decimal multiplied by a power of 10. For example, 6,500,000 can be written in scientific notation as 6.5 x 10^6.

Scientific notation consists of two main components: the decimal and the exponent. The decimal represents the significant digits of the number, while the exponent represents the power of 10 that the decimal is multiplied by. The exponent can be positive or negative, depending on whether the number is very large or very small.

To convert a number to scientific notation, you need to move the decimal point to the left or right until there is only one non-zero digit to the left of the decimal point. The number of places you move the decimal point determines the value of the exponent. If you move the decimal point to the left, the exponent is positive. If you move the decimal point to the right, the exponent is negative.

For example, to convert 0.00000025 to scientific notation, you would move the decimal point 8 places to the right, giving you 2.5. The exponent is -8, because you moved the decimal point 8 places to the right. Therefore, 0.00000025 in scientific notation is 2.5 x 10^-8.

Scientific notation is also known as standard form. It is a widely accepted format for expressing large and small numbers in a concise and unambiguous way. Using scientific notation can make it easier to perform calculations with very large or very small numbers, as well as to compare and analyze data.

 

Converting Numbers to Scientific Notation

Converting numbers to scientific notation is a process that involves expressing a number as a product of a coefficient and a power of 10. This form of notation is useful for expressing numbers that are either very large or very small. Here are the steps to convert a number to scientific notation:

  1. Identify the coefficient: The coefficient is the number that comes before the power of 10. It should be a number between 1 and 10.
  2. Determine the exponent: The exponent is the power of 10 that the coefficient must be multiplied by to get the original number. If the original number is a decimal, the exponent is negative.
  3. Write the number in scientific notation: Write the coefficient followed by “x 10^” and the exponent.

For example, to convert the number 3,456,000 to scientific notation:

  1. Identify the coefficient: The coefficient is 3.456.
  2. Determine the exponent: The exponent is 6, since 3,456,000 is equal to 3.456 x 10^6.
  3. Write the number in scientific notation: 3,456,000 = 3.456 x 10^6.

To convert a decimal number to scientific notation, the same steps apply.

Converting numbers to scientific notation can be useful when dealing with very large or very small numbers. In scientific notation, a number is expressed as a decimal between 1 and 10 multiplied by a power of 10. This allows for easier manipulation and comparison of these numbers.

To convert a number to scientific notation, one must first determine the appropriate power of 10. For large numbers, the power of 10 is equal to the number of digits to the left of the decimal point minus 1. For example, the number 123,456,789 would be converted to 1.23456789 x 10^8. In this case, there are 8 digits to the left of the decimal point, so the power of 10 is 8-1=7.

For small numbers, the power of 10 is equal to the number of zeros between the decimal point and the first non-zero digit plus 1. For example, the number 0.000000123 would be converted to 1.23 x 10^-7. In this case, there are 6 zeros between the decimal point and the first non-zero digit, so the power of 10 is -6+1=-7.

There are several tools available to convert numbers to scientific notation. One such tool is the Scientific Notation Calculator from Mathway 1. This calculator allows users to enter a regular number and automatically converts it to scientific notation. Another option is the Scientific Notation Converter from Calculator Soup 2. This tool provides multiple formats for the converted number, including engineering notation and word form.

Overall, converting numbers to scientific notation can be a useful tool when dealing with large or small numbers. By following the appropriate steps or using available tools, anyone can easily convert a number to scientific notation.

How to do Scientific Notation Solution

3 Simple Scientific Notation Examples

Scientific notation is a useful way of writing very large or very small numbers. In scientific notation, a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 × 10^8.

  1. Move the decimal place of the number to create a coefficient that is in between one and ten.
  2. Count the number of times that you moved the decimal. This will be the exponent on the power of ten.
  3. Moving the decimal to the left makes the exponent negative.
  4. Move the decimal to the right makes the exponent positive.

Here are a few more examples of scientific notation:

  • 0.0000000012 can be written as 1.2 × 10^-9
  • 12,000,000 can be written as 1.2 × 10^7
  • 0.00000001 can be written as 1 × 10^-8

Notice that in the first example, the exponent is negative because the number is less than 1. In the second example, the exponent is positive because the number is greater than 1. In the third example, the exponent is extremely negative because the number is very small.

Scientific notation is particularly useful in science and engineering, where very large or very small numbers are often encountered. It allows scientists to write these numbers in a compact and easy-to-read form.

 

5 Quick Scientific Notation Practice Problems

/5

Writing Numbers in Scientific Notation Quiz

Click Start to begin the practice quiz!

1 / 5

Convert the following to Scientific Notation:

3,850,000

2 / 5

Convert the following to Scientific Notation:

47,000

3 / 5

Convert the following to Scientific Notation:

80,000,000

4 / 5

Convert the following to Scientific Notation:

0.00093

5 / 5

Convert the following to Scientific Notation:

0.00476

Your score is

0%

 

The Role of Exponents in Scientific Notation

Scientific notation is a way of expressing very large or very small numbers using powers of 10. The exponent in scientific notation tells us how many times we need to multiply 10 by itself to obtain the number we are trying to represent. For example, the number 3,000,000 can be written as 3 x 10^6 in scientific notation.

Exponents play a crucial role in scientific notation because they allow us to express very large or very small numbers in a compact and convenient way. Instead of writing out all the digits of a large number, we can use scientific notation to express it with just a few symbols. This is especially useful in scientific and engineering applications where very large or very small numbers are encountered frequently.

To convert a decimal number to scientific notation, we need to count the number of significant digits in the number and then move the decimal point so that we have a number between 1 and 10. The exponent is then equal to the number of places we moved the decimal point. For example, the number 0.0000234 has three significant digits and can be written in scientific notation as 2.34 x 10^-5.

There are some rules for multiplying and dividing numbers in scientific notation. When multiplying two numbers in scientific notation, we can simply multiply the coefficients and add the exponents. When dividing two numbers in scientific notation, we can simply divide the coefficients and subtract the exponents. These rules make it easy to perform calculations with very large or very small numbers.

In summary, exponents play a crucial role in scientific notation by allowing us to express very large or very small numbers in a compact and convenient way. The rules for multiplying and dividing numbers in scientific notation make it easy to perform calculations with these numbers.

 

Scientific Notation for Small and Large Numbers

Scientific notation is a way of writing very small or very large numbers in a compact form. It is a shorthand method of expressing numbers as a product of a single-digit number and a power of 10. This notation makes it easier to work with numbers that are too large or too small to be conveniently written in decimal form.

Small Numbers

To write a small number in scientific notation, the decimal point is moved to the right of the first non-zero digit, and the number of places the point was moved is the exponent of 10.

 

Operations in Scientific Notation

Scientific notation is a useful tool for expressing very large or very small numbers in a concise and easy-to-understand way. However, performing mathematical operations with numbers in scientific notation can be a bit tricky. In this section, we will discuss how to add, subtract, multiply, and divide numbers in scientific notation.

Addition and Subtraction

When adding or subtracting numbers in scientific notation, the first step is to make sure that the exponents are the same. If they are not the same, you will need to adjust one or both of the exponents so that they match. Once the exponents match, you can add or subtract the coefficients (the numbers in front of the “x 10^” part).

For example, to add 3.2 x 10^4 and 2.5 x 10^4, you would first adjust the second number so that its exponent matches the first number:

3.2 x 10^4
+ 0.25 x 10^5
-------------
  5.45 x 10^4

Multiplication

To multiply two numbers in scientific notation, you simply multiply the coefficients and add the exponents. For example:

(2.5 x 10^3) x (3.0 x 10^4) = (2.5 x 3.0) x 10^(3+4) = 7.5 x 10^7

Division

To divide two numbers in scientific notation, you divide the coefficients and subtract the exponents. For example:

(6.0 x 10^6) ÷ (2.0 x 10^3) = (6.0 ÷ 2.0) x 10^(6-3) = 3.0 x 10^3

It is important to note that when dividing by a number in scientific notation, you should convert the divisor to standard form before dividing. This will make the calculation easier and more accurate.

In conclusion, performing mathematical operations with numbers in scientific notation is a straightforward process once you understand the rules. By adjusting the exponents and performing basic arithmetic operations on the coefficients, you can easily add, subtract, multiply, and divide numbers in scientific notation.

 

How to Convert to Scientific Notation FAQ

What are some examples of scientific notation with answers?

Scientific notation is commonly used in science and engineering to represent very large or very small numbers. Some examples of scientific notation include 3.5 × 10^4, which is equivalent to 35,000, and 1.2 × 10^-5, which is equivalent to 0.000012.

How can I do scientific notation in chemistry?

In chemistry, scientific notation is used to represent the very small numbers that are often encountered when working with atoms and molecules. To write a number in scientific notation, first determine the coefficient, which should be a number between 1 and 10. Then, count the number of places the decimal point must be moved to get the coefficient to this value. Finally, write the coefficient followed by “× 10^” and the number of places the decimal point was moved.

What is the process for doing scientific notation division?

To divide two numbers in scientific notation, divide the coefficients and subtract the exponents. For example, to divide 3.2 × 10^6 by 4 × 10^3, divide 3.2 by 4 to get 0.8 and subtract 3 from 6 to get 3. The answer is 0.8 × 10^3, which can be simplified to 8 × 10^2.

How do I use scientific notation in Excel?

To use scientific notation in Excel, enter the coefficient followed by the letter “E” and the exponent. For example, to enter the number 3.5 × 10^4, enter 3.5E4. Excel will automatically convert the number to scientific notation.

What is the method for doing scientific notation with E?

In some cases, scientific notation is written using the letter “E” instead of “× 10^”. For example, 1.2 × 10^-5 can be written as 1.2E-5. The process for converting a number to scientific notation using “E” is the same as the process for using “× 10^”.

How can I do scientific notation with fractions?

To write a fraction in scientific notation, first convert it to a decimal. Then, determine the coefficient and exponent as usual. For example, to write the fraction 1/100 in scientific notation, first convert it to the decimal 0.01. The coefficient is 1, and the exponent is -2 (since the decimal point must be moved two places to the left to get the coefficient to 1). The answer is 1 × 10^-2.

 

Converting to Scientific Notation Worksheet Video Explanation

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.

Free Converting to Scientific Notation worksheet download

Free Converting to Scientific Notation Worksheet

Enter your email to download the free Converting to Scientific Notation worksheet

Free math worksheets
Practice makes Perfect.

We have hundreds of math worksheets for you to master.

Get Started Now

 

Share This Page

the thinking cap newsletter logo