How to Write 1 Billion in Scientific Notation

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  • 0:02 Steps to Solve
  • 2:10 Solution
  • 2:23 Checking Your Work & Example
  • 4:11 Lesson Summary
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Lesson Transcript
Instructor: Laura Pennington

Laura received her Master's degree in Pure Mathematics from Michigan State University. She has 15 years of experience teaching collegiate mathematics at various institutions.

Scientific notation provides a way to write very large or very small numbers in a nice compact form. Let's look at how to write 1 billion in scientific notation. This lesson will illustrate the steps involved in this process, and we will also see how to easily check our work.

Steps to Solve

Scientific notation is a compact way to write very large or small numbers. In general, a number in scientific notation is a number, m, multiplied by a power of 10, and it takes the following form:


scinot1


The m is called the number part, and we multiply the number part by 10 raised to some number n, where n is an integer.

To write a number in scientific notation, we take the following steps:

1.) Locate the decimal point in the number. Move the decimal point to the location directly to the right of the first non-zero digit in the number. This new number will be the number part of the scientific notation.

2.) While moving the decimal, count how many places you move the decimal point and call it n. Also, note whether you are moving the decimal to the right or the left to get it to its final location.

  • If you move the decimal to the left, you will raise 10 to the power of n in the scientific notation.
  • If you move the decimal to the right, you will raise 10 to the power of -n in the scientific notation.

Putting these steps into practice will really help to solidify our understanding of how to write a number in scientific notation, so what do you say we do so by writing 1 billion in scientific notation?

In number form, we know that 1 billion is written like this: 1,000,000,000. The first step in writing this in scientific notation is to locate the decimal point.


scinot2


We see the decimal point is at the end of the number. The next step is to move the decimal point to the location directly to the right of the first non-zero digit in the number. In this case, the first non-zero digit in 1,000,000,000 is 1, so we move the decimal point directly to the right of 1.


scinot3


We see that 1 is the number part of 1 billion in scientific notation. Lastly, we need to figure out the number to which we are raising 10. To do this, we observe that when we move the decimal point, we move it 9 places to the left.


scinot4


This tells us that we will raise 10 to the power of 9.

Solution

We found that the number part of 1 billion in scientific notation is 1 and we raise 10 to the power of 9. This means that 1 billion in scientific notation is 1 x 10 9.


scinot5


Checking Your Work and Another Example

The great thing about the process of writing a number in scientific notation is that it is really easy to check our work and make sure we did everything correctly. All we need to do to check our work is to carry out the multiplication illustrated in the scientific notation.

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