Lesson 1 — Activity 3: Writing Numbers Using Powers of 10 and Scientific Notation


Getting Ready



Below is another look at a number and its place values.


           This image shows another example of the place values of a number.

Try This:


Show your knowledge of larger numbers once again:

  • Can you read the following number —   2,589,654?

  • What numbers are in the hundred thousands place, the ten thousands place, the millions place?



  • You would read the number as five hundred eight-nine thousand, six hundred fifty-four.

  • 5 is in the hundred thousands place, 8 is in the ten thousands place, 2 is in the millions place.



If you were given the number 100 and asked to write it another way, you could say that it was 10 × 10. This is another way of writing 100.

What if you were asked to write 100,000 another way? You could write it out in expanded form (10 × 10 × 10 × 10 × 10), but this would take a while.

Another way to write any number that is a multiple of 10 is to use powers of 10. Powers of 10 is a technique used to describe large or small quantities.


Let's look at the number 1,000,000. How many times do you have to multiply 10 by itself to get 1,000,000?

You have to multiply it six times. Using powers of 10, you can write 1,000,000 as

                 This image shows 10 to the power of 6.

The raised 6 is called an exponent. It just means there are six zeroes after the 1.


Take a look at this chart to see how different values are written as powers of 10.

Powers of 10 Chart





Notice on the chart that as the number becomes a decimal, that the exponent becomes negative.

This tells you how many digits will be written after the decimal.

For example, 10-1 means there is only one number written after the decimal place, so it would be written as 0.1.

If we went further, 10-4 means there are four numbers written after the decimal place, so it would be written as 0.0001.




There is a catch. Not every large or small number is a multiple of 10. This means we have to use another method to write them out a different way. This is called scientific notation.

Scientific notation is a number multiplied by 10 raised to an exponent.

Let's use the number 345 as an example.

  • To convert to scientific notation, first write it as

    345

    (In all whole numbers, the decimal point is to the right of the last digit. We do not place it unless it is needed. It would look like this: 345.)
  • Then move the decimal to the LEFT until there is only one number to the left of the decimal point:

    345.

    34.5

    3.45

  • Next, COUNT the number of times you moved the decimal place to the LEFT (two times in this example).
  • You would write 345 in scientific notation as: 

    3.45 x 102

                 

What about 8,975,000? Follow the same steps:

  • First write it as

    8,975,000.

    (Remember that in all whole numbers, the decimal point is to the right of the last digit. We do not place it unless it is needed.)
  • Then move the decimal point to the LEFT until there is only one number to the left of the decimal point:

    8,975,000.

    8,975,00.0

    8,9075,0.00

    8,975.000

    897.5000

    89.75000

    8.975000

  • Next, COUNT the number of times you moved the decimal place to the LEFT (six times in this example).
  • You would write 8 ,975,000 in scientific notation as:

    8.975 x 106


                    


So far, we have been working with whole numbers.
But what about numbers like these?


Examples of decimal numbers


You can write decimal numbers in scientific notation too. There's just a slight difference:

You would follow the same steps, except you count the number of places you move the decimal to the RIGHT and that is your exponent, which will be written with a negative number.


Let's look at 0.00065:
  • Move the decimal to the RIGHT until you have a number between 1 and 10.

    0.00065:

    00.0065

    000.065

    0000.65

    00006.5

  • Count the number of times you moved the decimal point to the RIGHT (four times in this example).
  • 4 is your exponent (It will be written as a negative.)
  • You would write 0.00065 in scientific notation as:

    6.5 x 10-4


                    

Images courtesy of www.imagesgoogle.com

Digging Deeper

Click here for more information on the powers of 10 and scientific notation.




Go to the next page to try a Self-check Activity on the powers of 10 and scientific notation.