Ravana had 10 heads
It was the day of Dussehra which is also called Vijaydashmi – the day of victory of Rama over the monster Ravana who had 10 heads. Many cities burn an effigy of Ravana at the end of this festive day. After watching the burning of the effigy, Tanya went to sleep. Suddenly she woke up scared, and shouted grandpa. Grandpa came and asked her what happened.
Tanya: In my dream I saw a monster with 10 heads and 10 hands. Whatever he sees, he breaks it up into 10 pieces. picks up each piece with one of his 10 hands and then puts it in one of his 10 mouths. Then the monster sees a mountain. It is very big. He breaks it into 10 small mountains which are still too big for his mouth. So he breaks each small mountain into 10 big stones so that he has 100 stones. He keeps breaking each stone into 10 pieces. Each time he does that, the stones decrease in size to one tenth but become 10 times more in numbers. One of the stones is about to hit me. I wake up. I am still scared.
Grandpa: Yes, because today you went to the Vijaydashmi mela and saw them burn the 10 headed effigy of Ravana.
Tanya: I am scared.
Grandpa: I will tell you a real story with the tens. I remember it well because one of the math teachers told us in school. You know one rupee has hundred paisas now.
Tanya: No one ever uses the paisa. It is worthless. It does not buy anything.
Grandpa: In the year 1955, the rupee was worth a lot more than it is today but it used to be divided into different types of coins. There were 64 paisas in one rupee. Four paisas used to give you one aana. Two aana coins or 8 paisa coins gave you a davannee. Chaar aana coins gave you a chavannee and 8 aana coins gave you an atthannee.
Tanya: That means for one rupee you got 2 atthannees, 4 chavannees, 8 davannees, 16 aanas or 64 paisas. It seems, each coin was half of the other. Did you also have a coin for half an aana?
Grandpa: Yes, it was called a takaa.
Tanya: What does this have to do with the 10 headed monster?
Changing the currency system in India
Grandpa: The government devised a new system. There were 100 naya paisas in one rupee. There were new coins for 1, 10, 25 and 50 naya paisas. Everyone who had the old coins could not just throw them away. For several years, the government let people use both types of coins. For now you go to sleep thinking about the coins. I will ask your mom, and tomorrow after school she will explain to you how to convert them from one type of coins into the other. Goodnight.
Tanya’s mind had gone away from the scary monster dream and she went to sleep. She was so fascinated by grandpa’s story and kept talking to her friends about it at school. The math teacher caught her talking in his class.
Teacher: Tanya. Don’t talk to the person sitting next to you. Come to the front of the class and tell everyone what is so interesting.
Tanya first thought that the teacher was getting angry with her and resisted but the teacher insisted that she come to the front. So Tanya was now in front and facing the class. She told the whole story of the change from a 64 paisa rupee to a 100 naya paisa rupee, and about the different types of coins before and after.
Teacher: Did your grandpa teach you how to convert between the old and the new coins?
Tanya: No. My mom is supposed to show me today after school.
How to convert into new currency
Teacher: Tanya, you told us an interesting story. So I think the whole class should learn how to convert. We will make this the lesson for today. Let us first think of this as a problem of fractions. I hope everyone paid attention to Tanya’s story. Who can tell me the old coins as fractions of a rupee?
Tinku: I always pay attention to what Tanya says because she is my best friend. She said that the old coins were worth 1/2, 1/4, 1/8. 1/16, 1/32 and 1/64 of a rupee.
Teacher: We are going to convert all these fractions into fractions of multiples of 10. For example 1/2 is equivalent to 50/100. So that means that the old half a rupee coin would be worth rupee 50/100. Because naya paisa was worth 1/100 of a rupee, there would be 50 naya paisas in the old half rupee atthannee coin. There is another way of writing the fractions. It is called the decimal system. In this system 50/100 = 0.50 or 0.5 because 50/100 = 5/10. So you can say that the old atthannee was worth Rs. 0.5. Let’s do them all this way because whichever coins you used, the value of the rupee was the same. So, Tanya convert a chavannee into the decimal form of a rupee.
Tanya: Chavanee = Rs. 1/4 = Rs. 25/100 = Rs. 0.25.
Teacher: Very good. Now Puru you do the davannee the same way.
Puru: Davannee = Rs. 1/8 = Rs. 125/1000 = Rs. 0.125.
Tinku raised his hand and said: Davannee is Rs. 0.125 and naya paisa = Rs. 1/100. So how many naya paisas will you get for a davannee?
Kate: I guess you could cheat and say either 12 naya paisas or 13 whatever benefits you more.
Teacher: No, the government set the price of the davannee at 12 naya paisas. How about an aana now, Manal?
Manal: This is a hard one. One aana = Rs. 1/16 = Rs. 625/10000 = Rs. .0625 or 6 naya paisas.
Tanya: I like it. That means addition and subtraction become easy once you have converted everything into decimal.
Adding fractions or decimals
Teacher: Good idea. I want the students in rows one and two to add 1/6 + 1/16 and then convert to decimal and rows three and four to convert to decimal first and then add. Make sure that when you add the decimals, the number of places match up in the terms you are adding.
Students from rows three and four are much faster and say 1/6 = 0.16666 and 1/16 = 0.0625 with the sum of the decimals being 0.22916. Later on, rows one and two say: 1/6 + 1/16 = 8/48 +3/48 = 9/48 = 22916/100000 = 0.22916.
Tinku raised his hand and said: Neither of the two answers is exact.
Teacher: Tinku, right now we will round off the terms.
The bell rang and the class was over. At home, Tanya’s mom was ready to teach her how to convert the coins of aana, chawannee etc. into naya paisas but Tanya taught mom instead. She told her that the teacher made her story into a math lesson. Tanya’s mom was happy and told Tanya to thank grandpa for the story and to tell him how the teacher used it in class.
Tanya talks about her scary dream
In the next class, Tanya raised her hand: Sir, my grandpa told me his story because I woke up with a scary dream. Now, I know that the dream fits into the decimal system. In my dream I saw a monster with 10 heads and 10 hands. Whatever he saw, he broke it up into 10 pieces. picked up each piece with one of his 10 hands and then put it in one of his 10 mouths. Then the monster saw a mountain. It was very big, I would say 1 kilometer long. He broke it into 0.1 kilometer long 10 mountains which were still too big for his mouth. So he broke each small mountain into 10 big stones so that he had 100 stones of 0.01 kilometer. He kept breaking each stone into 10 pieces. Each time he did that, the stones decreased in size to one tenth but became 10 times more in numbers. One of the stones was about to hit me. I woke up really scared.
Teacher: Tanya, you have given us a very good description of the decimal system except that it is not a monster. Now, I am going to give you some other examples. In the past the distance was measured in miles and now we use kilometers. You can convert one from the other. One mile = 1.6 kilometers. 1 kilometer is 1000 meters. Also, we can divide meter into smaller units: 0.01 meter = 1 centimeter and 0.001 meter = 1 millimeter. You have these marks on the scales which you use in your geometry class.
Weights and volumes in the decimal system
Puru: Sir, what about the weights? The old system was pounds and now we use grams, kilograms etc. It is again in the metric system. We also measure milk in liters and deciliters.
Teacher: Great. Now you know why to use the decimal system. As part of your homework you will convert the following fractions into decimals: 1/2, 100/8. 20/3 and 100//7. After that add them all up. Also, try adding them first and then converting into decimals? Which one was easier?
Apples cost 69 cents per pound. Your mom wants 5 kilograms of apples to bake pies. How much would the cost? Note that 1 kilogram equals 2.2 pounds.
Solution: 5 kg of apples = 5 x 2.2 pounds (lbs.) = 11 lbs.
At 69 cents or $0.69/lbs., the cost of 11 lbs. of apples = $7.59.
Complete the following equations. It will be easier if you use the answer from one equation for solving the next one.
1 + 1/2 =
1 + 1/2 + 1/4 =
1 + 1/2 + 1/4 + 1/8 =
1 + 1/2 + 1/4 + 1/8 + 1/16 =
1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 =
1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 =
1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 =
Did you notice that the sum keeps getting to closer to 2 as you go along?