Scientific notation is a convenient way of expressing large or small numbers. This lesson will explain the steps involved in writing 1 million using scientific notation.
We will then take a look at a real-world situation in which scientific notation is used to write 1 million.
Steps to Solve
We want to write 1 million using scientific notation. Writing 1 million using scientific notation involves the same steps as writing any number using scientific notation.
It’s simply a matter of counting decimal places, observing which way we’re moving the decimal, and then placing numbers in the right place. That doesn’t sound so bad, huh? Well, it’s not, so let’s get started!First of all, a number written in scientific notation is a number multiplied by a power of 10.
In general, the steps we use in writing a number x using scientific notation are as follows:
- Move the decimal point in x to create a number that is between 1 and 10. To do this, we move the decimal so that there is only one digit to the left of the decimal point.
That is, we move the decimal point in between the first and second digit of the number. The new number will be the number we multiply by a power of 10.
- Count the number of places you moved the decimal point in step one. This will be the number we raise 10 to. If we moved the decimal point to the left in step one, then the number we raise 10 to will be positive, and if we moved the decimal point to the right in step one, then the number we raise 10 to will be negative.
- Write the number using scientific notation with the information obtained in steps one and two.
Alright, let’s take the number 1000000 through these steps. The first step is to move the decimal point in 1000000 between the first and second digit. Therefore, we move the decimal point in between 1 and 0 in 1000000.
We see that the number we will be multiplying by a power of 10 is 1.The next step is to count the number of places we moved the decimal point and to observe the fact that we are moving the decimal point to the left.
|We have that we moved the decimal point six places to the left. Therefore, the power we raise 10 to is 6.Great! We’ve made it to the third step, which is basically just filling in the blanks. We’ve found that in the number a x 10 b, a is 1, and b is 6, so we have that 1000000 = 1 x 10 6.
See? You were right, it wasn’t very hard at all!
We’ve seen how to write 1000000 using scientific notation. Now let’s take a look at how this may be applicable in the real world. When it comes to scientific notation, it is used when we are working with very large or very small numbers. Using this notation makes working with these types of numbers much easier.Did you know that we all carry a whole bunch of bacteria in our gut? Millions, even billions! Sounds kind of gross, but it’s there! There is good and bad bacteria in our bellies, and ideally we want the good to outweigh the bad. We call the good bacteria probiotics, and nowadays, we can actually take probiotics as a supplement. We can also get probiotics be eating plenty of yogurt that has live active cultures in it.
This is an area where scientific notation is used to indicate the amount of beneficial bacteria in a supplement or yogurt.For example, a label on a yogurt may look something like the following:
Notice that the amounts of each type of bacteria is given using scientific notation, and because we just saw how to write 1000000 using scientific notation as 1 x 10 6, we know that there is 1000000 of each strain.
Probiotics are a great example of when scientific notation is used in something we may come across in our lives.
The good news is that the next time we are enjoying a yogurt, or decide to take probiotics, we now know how to read the label! We see that being able to read and use scientific notation is extremely useful, not only in the study of mathematics, but in our daily lives as well!