Every non-terminating repeating decimal expansion can be represented in (p/q) form where p and q are integers and q≠0

Let’s first start with the definition of rational numbers. I know that definitions in Mathematics appear to be boring but remember, they are the foundations of mathematics. The strength of your foundation will decide the heights of your mathematical concepts.

So let’s start with the definition.

A number ‘r’ is called a rational number, if it can be written in  form (p/q) where p and q are integers and q≠0

And there is one more interesting fact related to rational numbers. It is that non-terminating repeating decimal is a rational number. So obviously, every non-terminating repeating decimal expansion can be represented in  form (p/q) where p and q are integers and q≠0

Let’s observe this with the help of an example

Let a non-terminating repeating decimal expansion be 0.635635……

Let x=0.635635……

Multiply both sides by 1000


1000x=635+x       where  x=0.635635……


x = (635/999)

Where p=635 and q=999


Guide to Actuarial Science in India

Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in insurance, finance, and other professions and industries. It became a formal mathematical discipline in the late 17th century with the increased demand for long-term insurance coverage. William Morgan is known as the father of modern actuarial science. Those professionals who get trained in this discipline are called actuaries.

Actuarial analysis involves developing financial projections, cost-benefit analyses, and insurance plans. Actuarial analysts can work in a variety of industries but are mainly employed in the financial services and insurance sectors. This is a highly analytical role, requiring a great deal of data assessment and a keen understanding of probability and risk mitigation.

Actuarial consultant applies the extensive use of statistics, contingency plans, and large amounts of data to formulate a plan best suited to the client. They calculate and analyze the data, make forecasts, provide the most accurate information to clients and help them realize what there best options are. The purpose of actuarial valuation is to calculate the ‘ Present Value’ of payments that would be made to employees in future as part of an employee benefit plan.

Most actuaries love being an actuary because it allows them to use their talents and have a meaningful positive impact. There are other great reasons to consider a career as an actuary.

1. Actuary has consistently been rated one of the top jobs in the United States.

2. Actuaries earn great stating salaries that can double within first five years.

3. Students can get jobs even after clearing 3 or 4 actuarial exams.

4. Companies also support their employees for actuarial exams. Employees get incentives on passing each exam.

5. Actuaries enjoy certainty in uncertain times. They are always in demand as the world confronts risk.

6. Actuaries participate in high-level business decision making and solve real problems in every industry.

7. More than a fulfilling career,being an actuary allows you to maintain a low-stress, highly sought after work/life balance.

The eligibility criterion for pursuing actuarial career is that the candidate must have passed 10+2 exam. Then he/she must clear ACET exam to take the membership of the Institute of Actuaries of India(IAI). Many universities have undergraduate and graduate degree programs in actuarial science. IAI conducts the actuarial exams in various cities in India. Actuarial exams are divided into 2 types namely, written and practical.

Stage 1: Core Principles

CS1 Actuarial Statistics

CS2 Risk Modelling and Survival analysis

CM1 Actuarial Mathematics

CM2 Financial Engineering and Loss reserving

CB1 Business Finance

CB2 Business Economics

CB3 Business Management

Stage 2: Core Practices

CP1 Actuarial Practice

CP2 Modelling Practice

CP3 Communications Practice

Stage 3: Specialist Principles

Choice is introduced at this stage. The student will choose two subjects from the 8 subjects offered

SP1 Health and Care

SP2 Life Insurance

SP4 Pension and other benefits

SP5 Investment and Finance

SP6 Financial Derivatives

SP7 General Insurance Reserving and Capital modelling

SP8 General Insurance-Pricing

Stage 4: Specialist Advanced

The final stage of exams is one specialist subject chosen from

SA1 Health and Care

SA2 Life Insurance

SA3 General Insurance

SA4 Pension and other benefits

SA7 Investment and Finance

So there are total 13 exams to be qualified as an actuary. However, Indian students can also take membership of the Institute and Faculty of Actuaries(IFoA).

The insurance industry can’t function without actuaries. Private corporations rely on risk evaluation by actuaries. Actuaries help companies in designing pension and benefit plans, evaluate assets and liabilities, and stare down risk. They also work for the government too, helping manage its programs and overseeing public companies to ensure compliance with regulatory laws.

Important note: Students should start searching for actuarial jobs after clearing 2 or 3 exams. After joining the job, they can continue clearing the remaining Actuarial exams.

For further information, you can visit the website of the Institute of Actuaries of India


Spirit of Maths teacher in corona war

The coronavirus pandemic has gripped the whole world in its claws. In such a crucial time, along with the governments, several people and Non Governmental Organisations (NGOs) have been coming together to fight the virus in their own possible ways.

One such corona warrior is 85-years-old Maths teacher Saroja Sundararajan who has been contributing towards the Covid-19 funds by selling fun math activity sheets. It is a great example of a popular saying,’ where there is a will there is a way’.

Her passion for Maths helped her in exploring an innovative way to help those in need. As a teacher, she knows that students can better learn Maths concepts through fun techniques and interactive sessions. She has made learning of Maths for the students as easy and interesting as possible.

She integrates the subject with Art to enhance its beauty. She has started a website called Math Funds India. She used to introduce practical activities in classroom. The Department of Education of Delhi got so much impressed with her skills that they often sent their officers to attend her innovative classes.

She is the first Central Board of Secondary Education (CBSE) teacher to be awarded the Best Teacher’s National Award by President Zail Singh in 1986. She believes that every teacher should enter into the class with an interesting little idea of a story, a puzzle, a riddle or even an activity. This will definitely grab the children’s attention and they will start loving the subject.


Hop to the limits and continuity

Limits and continuity is a very important and basic concept in calculus. It should be understood properly to learn higher concepts.

When I started my honours degree, I enjoyed it thoroughly. I have started 5 day challenge for limit and continuity on my Instagram account. Every post will help in clearing this concept. Go and check out my Instagram account of ‘thanksmaths’ . Hope you will also enjoy this concept


Stimulus package

It is a package of economic measures put by the government to stimulate and strengthen the struggling economy. In this COVID -19 crisis, every country brought stimulus package to revive it’s economy. Recently, the Union Finance Minister Nirmala Sitharaman announced Atmanirbhar Bharat Abhiyan stimulus package of Rs. 20 lakh crores which is equivalent to 10% of India’s GDP.

It has broadly two objectives

  1. Minimising the human cost of COVID -19
  2. Converting this crisis into an opportunity by implementing structural reforms.

The stimulus package consists of fiscal support, monetary support, ease of doing business and some reforms such as

  1. The definition of MSME has been revised and the government will provide collateral free automatic loans of Rs. 3 lakh crore for a four – year tenure. There will be no principal repayment for one year.
  2. Government has reduced TDS rates by 25% and this will be enforced till March 31, 2021.
  3. Rs. 1.7 lakh package was given as relief under Pradhan Mantri Garib Kalyan package.
  4. Insurance cover of Rs. 50 lakh will be given to every health worker.
  5. Under MNREGA, wages have been increased from Rs 182 to Rs 202.
  6. Poor senior citizens, poor divyang workers and poor widows will be paid Rs 1000.
  7. Farmers will be paid Rs 2000 under Pradhan Mantri Kisan Yojana.
  8. RBI has reduced Cash Reserve Ratio and due dates of all IT Return filings have been extended from July 31 to Nov. 30, 2020.

Kindle Publishing – A way of earning Passive income

It is not possible to earn passive income instantly. It requires a lot of hard work and consistency. But this hard work is mostly at the beginning and once the system has started running, you will not be required to do much efforts. This is similar to constructing a building where approximately seventy percent of the time is spent on constructing only foundation.

Your next step is to experiment by considering well-calculated risks because eliminating risks is inevitable. In this, a lot of study and research will help you. After trying different things and observing their results, you will be able to analyse better options for you. You can eliminate and add certain things which suit you. Now comes the automation, which is actually a fun part.

One of the many ways to earn passive income is Kindle Publishing.

Kindle Direct Publishing is a platform where you can self publish your books with no cost. It is Amazon’s self publishing platform. It is the way to reach millions of readers worldwide. It makes your books available on Kindle Store within a few hours after uploading your materials.

There are many benefits of self publishing

  1. You don’t need to be authoritative figure or an expert in a particular subject in which you like to write.
  2. It removes our efforts to do network marketing or approaching influencers.
  3. It provides us space for experimenting and trying out a variety of niches.
  4. Most amazing, it provides passive income. After you have written and uploaded your book, wait for the sales to occur.

Our future challenge

Each milestone in business is achieved only once because everytime there would be different circumstances. When we create something new, we go from 0to 1 and when we go on adding something to it, we go from 1 to n. Creating something new is a miracle and miracles can happen through technology.

When we think about future, we hope for progress. There are two types of progress – horizontal and vertical. Horizontal progress is like going from 1 to n, means adding something to already familiar. Vertical progress is going from 0 to 1 means creating new things, which is much harder than horizontal progress.

Now, what is globalisation?

It is actually a horizontal progress, means taking those things that work somewhere and making them available to other parts of world.

Whereas technology is 0 to 1 progress. Technology is not limited to computers only. Instead, any new and innovative way of doing things is Technology. In this world of scarce resources, globalisation without new technology is not sustainable. So our challenge for future is to create new technologies to make 21st century way better than the 20th.


Book of Women mathematicians by Susan and John Edeen

Portraits of women mathematicians


Smallest & largest 3-digit number, Rounding off

One day, while teaching, I came across the concepts of forming smallest & largest two-digit or three-digit numbers and rounding off.

And I remember, when I was introduced to these concepts, I found them somewhat confusing.

But as the practice makes a man perfect. So I did and understood them. I have made a detailed video on these concepts. Watch it and also try to answer the riddle.

Also, subscribe my channel for further updates.


Book review – The Number Devil: A mathematical adventure

It is from the genre of fiction. The stories are fabricated around two characters of Robert and Number Devil 😈.

Watch the video for my detailed review.