Mrs. Diehl's Math Site

When you’re dealing with super large numbers, like a googol, wouldn’t you rather write them like this:

10¹⁰⁰

Instead of:

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

When we’re measuring the size of the universe or counting the numbers of sand on a beach, it’s just easier to use scientific notation.

Here’s a review of our lesson.  Links to extra problems are at the end of this post.

First, students remembered a book we read the previous week about “power counting.”

After reading this book, students wrote the names, standard notation, and scientific notation for numbers up to googolplex in a graphic organizer.  Then students worked on finding the patterns and rules to determining the scientific notation for a number.

Students quickly pointed out that the “power” of 10 was always the same as the number of zeros following the 1.  So for one billion, the standard notation is:

1,000,000,000

There are 9 zeros so the scientific notation is

10⁹

which is the same as

10×10×10×10×10×10×10×10×10 (10 multiplied by itself 9 times=10⁹)

Then, I asked the students how they might show a number like this in scientific notation:

6,000,000

We knew that 1,000,000=10⁶.  Students used this information to make guesses for 6,000,000.  They offered 60⁶  and 6⁶.  Students used their calculators to see that 60⁶=46,656,000,000 (TOO BIG!) and 60⁶=64,656 (TOO SMALL!).

^{So we found that we had to multiply 6 times the scientific notation for one billion because 6×1,000,000= 6,000,000}

6,000,000 = 6×10⁶

Students practiced changing similar numbers from standard notation into scientific notation.

Then, we encountered another problem.  What if we have a number like this 5,600,000,000?  How do we show it in scientific notation?

Students thought this might be 5×10⁸ or 56×10⁸.  We plugged those numbers in the calculator.  56×10⁸ worked, but we learned that the first number that we multiple with the power of 10 must be less than 10.

We learned to write scientific notation using decimals.

5,600,000,000 = 5.6×10⁹

The power of 10 is still the amount of numerals that come after the first numeral (there are 9 numerals after the numeral 5 in 5,600,000,000). However, we multiply by the first number with a decimal followed by the next numerals until we get to our string of zeroes.

Here’s a step by step visual:

First, take a look at the number.

Next, pull out the numerals before your string of zeroes.  Put a decimal after the first numeral.

Now, multiply by 10 to the power of however many place values there are after your decimal.

For some extra practice with scientific notation, try “Dad’s Worksheets” here, and here.

What questions remain about scientific notation?  Is there anything that doesn’t make sense? Leave your questions in the comment section.