The Rule of 49 II Find Unit Digit of Large Expressions II Simple but Important

[00:00:02]Hello friends. Welcome to Suresh Agarwal's mathematics shortcuts. A very important concept for all the quantitative aptitude exams and you know the students struggle so much. But if they are aware of the basic rules to crack such questions, the questions are not difficult, right?

[00:00:19]So what what is the concept which I'm going to take up for this video?

[00:00:23]This is called finding the unit digit.

[00:00:27]When you are given a large expression especially involving exponents and you have to find the unit digit of that expression, how do you crack that? You know, you have three different rules and in this video I'm going to stress on one rule which is known as the rule of four and nine or sometimes we call it the rule of 49.

[00:00:48]Now what is this rule of 49 and how does it it help us in finding the unit digit of big expressions? I'll explain everything and before that let me tell you that the rule of 49 is a part of our ultimate guide to speed maths which is available now and I'll show you a glimpse of that book also. But before you know, getting into the details of the book, I need to tell you the rule of 49 and where does it apply?

[00:01:15]So the concept here is you have an expression like suppose you have 2,194 raised to power 713 and let's multiply this by 4,229 raised to power say 8,194.

[00:01:34]And I need to find the unit digit of this expression. See, uh there has to be a logic, right? Because the exponents are big, the numbers are big.

[00:01:43]So the first important rule when you are doing the rule of 49, see I'll come back to this question later and I'll solve that in 3 seconds time only without use of pen and paper. But let's understand the basics first.

[00:01:58]Whenever you have a number ending in four in the base and the power is odd, then the unit digit of this expression is going to be four only. Like four raised to power one is four, four raised to power three is 64, which again ends in four. Four raised to power five will again end in four only. So, whenever the base has unit digit four and the power is odd, unit digit will always be four.

[00:02:28]Likewise, if the unit digit is four in the base and the power is even, just like four squared, four squared is 16, that ends in six, right? And therefore, whenever you have an even power with, uh, you know, the base ending in four, the answer will always have at the unit digit six.

[00:02:50]Likewise, what about nine? When I say rule of 49, I took up four here, now I'm going to take up nine.

[00:02:59]So, we'll have a nine here and and odd power, and then again nine here and then even power.

[00:03:07]Now, you can guess very easily. Nine raised to power one, nine raised to power three, all end in nine only. Nine raised to power two is 81, so it ends in one.

[00:03:18]So, rule of 49 states that when the base is either four or nine and the power is odd, then the base or the unit digit remains equal to the base, that is nine remains nine, four remains four.

[00:03:33]But, when the power is even, the base both four will yield, uh, unit digit six and the base nine will yield a unit digit of one.

[00:03:44]Now, this is called the rule of 49. Now, I'm going to solve some questions and before that I need to show you the ultimate guide to speed maths volume one and ultimate guide to speed maths volume two.

[00:03:56]These books are released now and available to be delivered at your door steps. They contain 350 smart and short tricks containing 28 different topics which are asked in quantitative aptitude and students from class five onwards can study these books.

[00:04:14]So if you want to make your child smarter in handling the calculations, then you need to get hold of this. Video links are also given 2,400 practice questions, 1,300 practice questions.

[00:04:26]Everything, you know, and 10x faster speed of calculations, easy language targeting competitions like NTSE, banking, railways, SSC, IMO and then you know, the Aryabhata Ganit Challenge conducted by CBSE and other competitive exams, you know. And if I show you a glimpse, here is the volume one. This is volume one. And this is the volume two.

[00:04:53]So these two books will be a treasure house of knowledge for all of you. And if I show you inside, look at this. If I open any random page, it will have lots and lots of video links. All these are video links and challenge zones and then the answer key are also given. So wonderful, wonderful compilation of short tricks for all of you at a nominal cost. How do you get a copy? You can send me a message on WhatsApp. This is the WhatsApp number 9896369963.

[00:05:21]Or you can click the Amazon links given in the description of this video so that you know, you can place your orders orders safely from Amazon.

[00:05:30]So friends, what are the questions based on this? So we can we can have so many different questions, you know, odd and even type of. Like suppose you have the base four, suppose 314 with a odd power here. So I'll take odd odd, okay? Four questions and we will be done with the trick.

[00:05:52]So, let's have the base four like this.

[00:05:56]Um like this.

[00:06:01]And like this, okay? And then we will have a base maybe nine or you can combine it with four only.

[00:06:13]Like four and four.

[00:06:15]Um say 7164.

[00:06:19]Four and four, then four and nine, 11 39.

[00:06:25]And then four and we have done four and four, four and nine. And then we can combine like many many other different examples. I've taken all fours, so we can take some more examples like 29.

[00:06:38]And then 84.

[00:06:40]Now, powers are important. What will happen if you have a power odd here, say 83, and odd here, say 713.

[00:06:50]Odd here, say 107.

[00:06:54]Even here, say 84.

[00:06:57]Um you can take even and even like 1122 and 712, right? Even even.

[00:07:05]We have done odd odd. We have taken odd even. We can take even odd like 718 and odd means 817, okay? Now, all these expressions have a product in between them and I can find the unit digit so very easily.

[00:07:24]See here, we have four with a odd power, so this remains four.

[00:07:31]>> [clears throat] >> Four with an odd power remains four. 4 * 4 is 16, so the answer is six.

[00:07:38]Four with an odd power remains four.

[00:07:41]Nine with an even power becomes one. So four into one becomes four as the answer.

[00:07:49]Four with an even power becomes six because four squared is 16. Nine with an even power becomes one. So six into one answer ends in six.

[00:08:02]Likewise four with an even power becomes six.

[00:08:06]And four with an odd power remains four. So six into four 24 which ends in four. So the unit digit is four.

[00:08:17]I wrote a question in the beginning of the video. I'll show you this question.

[00:08:21]Can you solve this now? Very easily, right? Four with an odd power remains four.

[00:08:28]And nine with an even power becomes one.

[00:08:31]So the answer is four into one. Four is the unit digit of this expression.

[00:08:36]So friends, you know, knowing the trick is one thing and understanding how this works is based on how much you are applying the trick to solve the questions. There are two more rules for cracking the unit digit of any expressions. So keep watching the series of videos. I'll come up with those also. In the meantime, you can go for the speed maths books. The Amazon links are given here and do practice this concept the rule of 49 and tell me in the comments below is it working for you. All the best.