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Recent Articles Decimal to Percent Sep 29, 20 10:58 AM Learning how to convert a number from decimal to percent is the goal of this lesson. Read More

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The main difference between base five numeration system and our familiar base 10 numeration system is that grouping is done in groups of 5 instead of 10.For instance, to represent 24 in base 10 using sticks, you could use two groups of ten and 4 as shown belowHowever, to represent the same number in base 5, you make groups of 5Notice that you have 4 groups of five and 4. You write 44or 44Thus, 24= 4444! You don't read it as forty four because this is how you read four tens and four in base 10. We are not in base 10 anymore.44is read four four base 5In like manner, if you group 17 in groups of five, you can get three groups of 5 and 2You write 17= 32and 32is read three two base 5Look at the following pattern:19= 3418= 3317= 3216= 3115= ?What do you think 15 is in base 5?Yes, 15= 30= ?This is important. It is not 3 just because we have three fives in 15In fact, what it means is three fives in the second place value and zero number in the first place valueThe first ten base 5 numerals are shown below:101112131420Notice that the first four numbers have the same representation in base 10 and in base 5The second difference between base five and base ten is that in base ten, we use the 10 digits 0, 1, 2, 3 , 4 , 5, 6, 7, 8, and 9In base 10, when you have 10 tens, you replace it by one hundred and starting from the right one hundred is in the third positionIn general, place values are power of 10: 10= 1, 10= 10, 10= 100, 10= 1000, etc. representing first, second, third place etc respectively.On the other hand,In base 5, we use only 5 digits 0, 1, 2, 3 , and 4In base five, when you have 5 fives, you replace it by one twenty five and starting from the right twenty five is in the third positionIn this case, place values are power of 5: 5= 1, 5= 5, 5= 25, 5= 125, etc representing first, second, third place etc.respectively..Having said that, what is 57 in base 5Group 57 in groups of 25 and 557 has 2 groups of 25, 1 group of 5 and 2, so 57= 212