How Fraction and Decimals are the same

” What are you learning at School these days?” I recently asked some 4th graders..”Oh we just finished fractions and are now doing Decimals..” They told me..” Well do you know that fractions and decimals are the same thing” I poked a little just to check whether they are being given the conceptual knowledge.. “How can they be the same thingy?” One of the 4th grader piped up..”They are both different things really? Are you guys sure about it? Ok tell me how are these different?” “Welllll..they just are..” ” but how ?” I persisted..” Ok why don’t you tell us how these are the same?” They finally asked.

This was an opportunity I was waiting for.. I asked them ” Do you know that in greek DECA means if we talk about a Decade it means 10 years or if you have heard of the Decathlon in Olympics Decathlon is the combination of 10 events..I am sure you know that our number system is based on 10’s. i.e if we have to write 256 you can write it as 200+50+6?”

” Yes of course” They said. ” Do you know number 10 plays an important part in the numbers which are less than 10?” I said. ” How ?” They asked me immediately.

” Ok , lets take an example…Ussain Bolt holds the world record of 100 meters race which he completed in 9.58 seconds in 2009. here if you see we have 9 whole seconds and then there is a POINT which we call as decimal and then we have 58 after the decimal which is actually part of the whole after the decimal point the first number that comes is 1/10th of a number or we can write it as 0.1. The next number is 1/100th of a number which we can write as 0.01. Lets see what happens when we divide lets say 200 by 10

Place value in Decimals: The above can be explained as given below

200/10 = 20 We can see once divided the digit has moved to 10’s place

20/10 = 2 – here the digit has moved to the ones place

2/10 = 0.2 – The digit has become 2parts of 10’s and has moved to the 1/10th position

0.2/10= 0.02 – The digit has become 2 parts of hundred or 2/100th

0.02/10 =0.002 -The digit has become 2 parts of 1000 or 2/1000th part

“Did you notice that each time we divide the number by 10 the digit shifted one place to the right” I asked..” Yes its like slides almost..”

” So now If we go back to Ussain Bolt we understand that 9.58 is actually 9 full seconds and 58th part of the hundred so we can also write 0.58 as 58/100 or if we have to expand and write the same we can write it as

0.5+0.08 = 0.58. So if you notice the first part is 5 parts of 10 and the second part is 8 parts of 100…

“No one told us like this ..this is really if my teacher gives me 0.25 it will actually me 25 parts of 100, wow.. that means 1/4..”one of them who was faster with calculations said..”Yes it means exactly that.. ”

I was satisfied that conceptually they understood the concept..I made a mental note of teaching them the relation between Ratio, Proportion, Fraction and Percentage next time

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