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Decimal system refresher
Review how the decimal number system works before diving into the binary number system. The decimal number system and binary number system work the same way; the only difference is what each digit represents (0-9 versus 0/1). Created by Pamela Fox.
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The decimal system works well for rational numbers, but what about irrational numbers like Pi? Is there a way to show these numbers in the decimal system? Or, is the decimal system inherently limited to representing certain kinds of numbers (e.g., rational numbers)?(8 votes)
The decimal system cannot fully express irrational numbers as all irrational numbers will require an infinite number of digits to be completely written out. The decimal system can only write out rational approximations for irrational numbers by rounding after a certain number of decimal places.(8 votes)
what about irrational numbers like Pi?(2 votes)- This is an excellent point. Irrational numbers have infinite representations, so they can only be approximated by finite representations in computers.
so Pi would be truncated to something like 3.1415 instead of 3.14159265...
Hope this helps(10 votes)
what is a decimal system(0 votes)
The decimal system contains 10 digits, 0 through 9. The binary system contains digits, 0 through 1. A decimal number is 69, while the binary number is1000101. Because binary has a smaller repository of digits, the numbers contain more places.(2 votes)
- what about irrational numbers?(4 votes)
- they are cool(0 votes)
The decimal system works well for rational numbers, but what about irrational numbers like Pi? Is there a way to show these numbers in the decimal system? Or, is the decimal system inherently limited to representing certain kinds of numbers (e.g., rational numbers)?The decimal system cannot fully express irrational numbers as all irrational numbers will require an infinite number of digits to be completely written out. The decimal system can only write out rational approximations for irrational numbers by rounding after a certain number of decimal places.what about irrational numbers like Pi?This is an excellent point. Irrational numbers have infinite representations, so they can only be approximated by finite representations in computers.
so Pi would be truncated to something like 3.1415 instead of 3.14159265...(2 votes)- The decimal system works well for rational numbers, but what about irrational numbers like Pi? Is there a way to show these numbers in the decimal system? Or, is the decimal system inherently limited to representing certain kinds of numbers (e.g., rational numbers)?(1 vote)
why are we doing this?(1 vote)- How is it used(1 vote)
- what about number that go on and on(1 vote)
what about the fractions numbers?(1 vote)
Video transcript
- [Instructor] Let's
star with the refresher of the decimal system. Since understanding decimal will help us to understand binary. Consider this number 234. We often say that the
four is in the ones place. The three is in the tens place. And the two is in the hundreds places. That makes this number equal to two times a 100, plus three times 10, plus four times one. All equal 234. Now we can also say that this ones place is 10 raised to the power of zero. The tens place is 10
raised to the power of one. And the hundreds place is 10
raised to the power of two. If we're going to add another place here, this would be a 1,000 and
that would be the same as 10 raised to the power of three. Each place represents a power of 10. And that's why this is the decimal system from the Latin for 10. To figure out what
number we're looking at, we just look at the digit
that's in that place and we multiply it times its place. So a one here would be one
times a 1,000, plus 234. And that's the decimal system.