Chapter 6: Decimals 81MATH IN THE PAST
Pi is the name given to the ratio of a circle’s circumference, the measurement around
the circle, to its diameter, the measurement across the widest part. Pi has a long
history. There is evidence that mathematicians were thinking about this number in
ancient Babylon, Egypt, Israel, Greece, China, and India, but all of them came up
with different values a bit more than 3. Today, mathematicians have calculated pi to
trillions of digits. Still no pattern.The rational numbers and the irrational numbers
together make up the real numbers. The real
numbers include all the other sets of numbers
we’ve looked at. We started with the counting
numbers and then got more complex. The
irrational numbers are the first set that doesn’t
overlap the ones you’ve met before.
You might picture the set of real numbers
something like this:
Rational NumbersIrrational
Counting Numbers
NumbersIntegersWORLDLY WISDOM
Are there fake numbers? If the rational numbers and the irrational numbers combine
to make up the real numbers, are there numbers that aren’t real numbers? Actually,
mathematicians will tell you that there are, but they don’t call them fake. They call
them imaginary numbers, because they aren’t real numbers, but you can imagine them.
You know that 2^2 =^4 , and it’s also true that (-2)^2 =^4 , but what number can you square to
get -4? Most people would say there is none, but if you let yourself imagine it, there can
be a -^4.The Least You Need to Know
- The decimal point separates whole numbers on the left from fractions on the right.
As you move to the right, the value of each place is divided by 10. - To write a small number in scientific notation, write it as a number greater than or
equal to 1 and less than 10 times a negative power of 10. - Performing arithmetic operations with decimals is very similar to performing
arithmetic operations with whole numbers.