8 Part 1: The World of Numbers
To write powers of ten in a more convenient form, you use exponents. These are small numbers
that are written to the upper right of another number, called the base, and tell how many of that
number to multiply together.
If you want to show 3 v 3, you can write 3^2. In this case, 3 is the base number and 2 is the
exponent. This notation tells you to use two 3s and multiply them. We’ll look at exponents again
in a later chapter, but for now we’re going to take advantage of an interesting result of working
with tens.DEFINITION
The expression power of ten refers to a number formed by multiplying a number of 10s.
The first power of ten is 10. The second power of ten is 10 v 10 or 100, and the third
power of 10 is 10 v 10 v 10 or 1,000.
An exponent is a small number written to the upper right of another number, called
the base. The exponent tells how many of that number should be multiplied together.
You can write the third power of 10 (10 is 10 v 10 v 10) as 10^3. In this case, 10 is the
base number and 3 is the exponent.When you multiply tens together, you just increase the number of zeros. 10 v 10 = 10 0,
10 0 v 10 = 1000. Each time you multiply by another ten, you add another zero. Look at a place
value, count the number of zeros in the name, and put that exponent on a 10, and you have the
power-of-ten form of that place value.Powers of 10
Decimal Place Value Number of Zeros Tens being multiplied Power of Ten
ones 1 0 None 100
tens 10 1 10 101hundreds (^100210) v 10 102
thousands 1,000 3 10 v 10 v 10 103
Using this system, a million, which you write as 1,000,000 in standard notation, has 6 zeros after
the 1, so it would be 10^6. One hundred trillion is 100,000,000,000,000 or a 1 followed by 14 zeros.
You can write one hundred trillion as 10^14 , which is a lot shorter.