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