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What is the Difference Between Rational and Irrational Numbers

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If you’re unsure about the difference between rational and irrational numbers, keep reading to discover a simple guide to understanding the key differences between rational and irrational numbers.

What is the difference between rational and irrational numbers?

The primary difference between irrational numbers and rational numbers is that a rational number can be easily expressed as a whole fraction.

A rational number can always be turned into a fraction, which has both a full numerator number and a full denominator number. While an irrational number can’t be expressed as a whole fraction and can’t be written down as a simple ratio of two integers.

Are there any other noticeable differences between rational and irrational numbers.
Yes, while irrational numbers can’t be written down as simple, whole fractions, irrational numbers can easily be expressed as decimal numbers.
Furthermore an irrational number features endless non repeating digits after it’s decimal point. An example of an irrational number is pi which is most commonly shortened to 3.14159. Keep in mind that it is impossible to express a never ending decimal number such as pi with a simple fraction.
To cement the knowledge that you’ve just read, another example of a recurring infinite decimal number, which can be referred to accurately as a rational number is the golden ratio, which is sometimes shortened to 2.7182818.
Everything you need to know about the major differences between rational and irrational numbers:

1. There are infinite irrational numbers
You may be surprised to hear that there is at least one irrational number between any two rational numbers.

2. Every whole number is a rational number.

If you’re confused about whether the number zero is a rational number, the answer is yes because zero and any other whole number can be divided by the number one, which makes zero a rational number.

3. Decimal numbers tend to be irrational numbers, however there are exceptions

Decimal numbers such as pi also tend to be irrational numbers as they aren’t whole numbers and therefore can’t be divided using a whole numerator and a whole denominator.

However there are exceptions. As an example, recurring decimal numbers such as 0.26262626 are rational numbers.

If in doubt, remember that decimals which are infinite and don’t feature a number sequence are irrational numbers, while decimal numbers which feature recurring numbers such as 0.26262626 are always classed as rational numbers.

4. Negative whole numbers are also classified as being rational numbers

If you were confused by negative whole numbers and whether they are rational numbers or irrational numbers the answer is that negative numbers such as -6 can still be easily divided by themselves and therefore can be expressed by whole fractions and are rational numbers.

5. Square roots can also be irrational numbers

Another example of a common irrational number which has not been discussed above are square roots, which can also be irrational numbers.

After reading the definitions and tips which were listed above, you should now be confident about being able to class both rational numbers and irrational numbers.

How to Save Money: The Easy Way

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In order to discover how to save money without a whole lot of effort, continue reading to discover some of the simplest ways to save money!

How to save money: The easy way

1. Remember to budget for incidental items that change from month to month

Many individuals fail to budget for incidental items that aren’t part of their regular monthly budgets, which can place a strain on their budgets. So ensure to factor in incidental costs into your monthly budget. As an example, make sure to budget money to purchase your friends and family members birthday gifts.

2. Don’t give in to the urge to impulse shop

If you’re often tempted to purchase items on a whim, it’s a great idea to avoid impulse shopping. Next time you find yourself tempted to purchase an item which you saw in a shop window or on one of your favorite online websites, wait at least 24 hours before purchasing the item which you have in mind.

As you’ll normally find that within 24 hours, you’ll think twice and will decide that you don’t really need the item that you were ready to blow your budget, to purchase.

3. Borrow items from friends and family members, instead of purchasing them

As an example, if you’re looking to go on a road trip and are considering purchasing items such as a bicycle, a tent and a blow up mattress, it’s well worth asking your close friends and family members whether they have some of the items which you need. As most of your loved ones will be more than willing to help you out and to loan you the items which you require.

4. Don’t be afraid to purchase pre loved items

One way to save thousands of dollars each year is to purchase pre loved items such as clothes and accessories and furniture. As an example, you can often get great deals on items that you’re looking for on online auction sites such as eBay and at local yard sales and thrift stores.

If you’re worried about your friends judging you for buying preloved items, the truth is that your friends probably won’t be able to tell that you’re purchasing preloved items, especially if you purchase items which are in great condition.

If you’re lucky you may even come across items that have never been used before at a fraction of their original recommended retail price.

5. Choose one day a week, where you don’t spend money

It’s a great idea to choose one night a week where you rely on free activities to entertain yourself rather than spending money at a movie theatre or going out for drinks with friends.

As an example, you may enjoy taking a walk along a nearby beach or playing card games or board games with your friends or family. Once you discover how much fun you can have without spending money, you may find it easier to spend less money the rest of the week.

So if you’ve been on the lookout for easy ways to save money, it’s well worth getting started with the five money saving tips listed above.

How to be Successful: A Fool Proof Guide

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If you’re focused on achieving your goals and are looking for a simple yet effective guide to becoming successful, you’ve come to the right place.

How to be successful: A fool proof guide

1. Write a detailed plan of the actions which you need to take to meet your goal

Successful individuals usually have one thing in common, they plan to succeed. One of the best ways to plan to succeed and to meet your goals is to ensure that you have a detailed plan of action to follow. Included in your plan should be short term goals, which you should achieve each month and each week, in order to get closer to meeting your ultimate long term goal.

2. Talk to individuals who have already obtained the success which you plan to achieve

In order to avoid some of the pitfalls on your route to your goal, it’s well worth arranging to talk to a couple of individuals who have already obtained the success which you plan to achieve yourself.

As an example, if you’re interested in getting into business, it’s well worth tracking down an experienced business mentor, who’ll be able to help you avoid making unnecessary mistakes, while providing you with tips and tricks, which may help you achieve your goals a little faster.

3. Don’t be afraid to ask for help

Contrary to popular belief you don’t have to achieve success entirely on your own merit. While you won’t be successful unless you give 100% of your energy, focus and passion to your goals and endeavours, most successful individuals aren’t afraid to ask from help and to obtain information and advice from to others.

4. Make sure to ask the right individuals for help

Just be sure to ask the right individuals for assistance. As an example, if your goal is to run your first marathon, it may be worth reaching out to a running coach and a dietician, to help you meet your goals but it may not be a wise idea to ask for assistance from negative friends or family members, who may not believe that you can achieve your goal of running a marathon.

5. Identify your strengths and weaknesses

By identifying your strengths, you’ll be able to use your innate strengths to your advantage and if you successfully identify your weaknesses, you’ll be able to work on turning the skills which you’re currently weak at into strengths.

6. Don’t be afraid to alter your plans

As you start taking actions to meet your goals, you may find that you may need to alter your original plans from time to time. So, just make sure that you’re not rigid when it comes to following plans and that you have enough sense to be able to adapt your plans on your journey towards success.

7. Celebrate every success

Instead of waiting until you’ve reached your end goal, increase your motivation to meet your ultimate goal by remembering to mentally celebrate each success and milestone which you tick off!

So no matter what your goal or passion is, it’s well worth using the tried and tested tips listed above, which will help you get on track to meeting your goals.

6 Business Marketing tips that are well worth Trying Out

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In order to discover a few new marketing techniques will can increase your business’ sales and profit, simply continue reading.

6 Business marketing tips that are well worth trying out:

1. Reuse information from your previous marketing campaigns

As an example, you may want to reuse information from one of your business’ blog pieces to create a marketing video. Or you may want to reuse well shot images of your business’ products and services which you’ve posted on your website, to create new social media posts for your business’ various social media accounts on Twitter, Facebook and Instagram.

2. Use competitions to attract attention

An easy way to attract attention to your business’ social media accounts is to use simple competitions, to encourage individuals to follow your accounts or to make purchases on your business’ website.

As an example, you may may want to run a competition which offers individuals the chance to win a new product which is due to be released in the coming weeks or you may want to offer your customers the chance to win the back the value of their last purchase with your business. You may even stipulate that entrants must follow your business’ social media pages or sign up to an email subscription list.

As most individuals have a tendency to be tempted to win something for nothing, you should have no trouble attracting plenty of entries. You may even be interested in offering double entries for individuals who share your original social media post on their own social media account.

3. Try to win an online business award to post on your social media pages and website

If you manage to win an online business award in your industry, you may may be able to advertize your award on your social media accounts and your website. If winning an established business award seems a little far fetched for your business, you may want to start up your own business awards for businesses in your city or area.

As a bonus, if you start your own business awards, you may form valuable industry contacts with other businesses in your industry who aren’t in direct competition with your business and offer different services or products to your business.

4. Carefully use guerrilla marketing techniques

If you haven’t heard of the term guerrilla marketing, it involves using street advertising to market your business’ online presences. As an example, you may want to use chalk to write your business’ social media handles on the pavement outside your real life store. Or you may want to put up give out business cards that have your business’ website and social media links, printed on them.

5. Create a monthly or weekly newsletter

One way to keep your customers well informed of new products and services as well as sales is to create a monthly or weekly newsletter, which you can encourage your customers and followers to sign up to.

6. Make sure that your emails and newsletters offer valuable content

If your emails and newsletters offer valuable content, individuals will be far less likely to unsubscribe from your business’ marketing emails.

Hopefully you’ve discovered at least one new marketing technique which you believe can increase your business’ sales and profits.

7 Business Budgeting Tips

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In order to take control of your business’ finances, it’s a great idea to work on budgeting for your business’ future.

7 Business budgeting tips:

1. Overestimate your business’ operating costs

One of the worst mistakes which you can make, when it comes to creating a realistic, workable budget for your business is to underestimate your business’ operating costs. Remember that it’s always a better idea to slightly overestimate your costs than to underestimate your business’ costs and to run out of funds to run each area of your business effectively.

2. Make sure that your business has an emergency fund available

It’s well worth ensuring that your business has a healthy emergency fund, which is kept seperate from your business’ day to day accounts. Having an emergency fund available, may come in handy if any unexpected costs arise or if you want to upgrade your business and to take your business to the next level.

3. Make sure that you’re not getting overcharged by your current supplier

Even if your business has a long term supplier, who you’re used to dealing with, it’s always a smart idea to get quotes from other suppliers who may be able to provide your business with the same quality product as your current supplier for a much lower price.

4. Try and predict how your sales numbers may change in the next 12 months

One way to create an accurate budget is to try and predict how your sales numbers may change over the next 12 months. As an example, when you look at your business’ sales statistics for the last 12 months you may notice that your sales increase in the months that lead up to Christmas or that you sell more products or services during a particular season such as summer.

5. Save a set percentage of your profit

It’s well worth deciding on a set percentage of your profit, which you’ll save in your business’ emergency fund, each year. If your profits are particularly healthy one year, you may also want to increase the amount of money which you save for a rainy day or to take your business to the next level.

6. Make sure to work on paying off your business loans

Your end goal should be to have zero debt. As you know it’s also wise to pay off your loans as quickly as possible, in order to avoid paying high levels of interest on your business loans. So it’s a great idea to invest a fair amount of your business’ profits in to getting on top of your business debt.

7. Make sure to review your business’ budget on a monthly basis

instead of setting a year long budget and not looking at your budget for 12 months, it’s a wise idea to review your business’ budget on a month to month basis. As you may have to tweak your budget, multiple times over a calendar year.

So if you’re a business owner who is looking to budget for the financial future of your business, it’s a great idea to implement many of the budgeting tips listed above!

Travel and education: Study abroad tips

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If you’re planning a study abroad trip, continue reading to discover a few handy tips that will make your time overseas a whole lot easier!

Travel and education: Study abroad tips

1. Purchase a journal to write about your daily experiences living abroad

It’s well worth going out and purchasing a journal which you’ll be able to pack for your study abroad experience. As while you can write about your daily experiences as an international student using a digital diary, as the years go by, you’ll love being able to read a physical diary of your experiences abroad.

You may want to place trinkets such as ticket stubs to sports game or concerts which you attend as well as polaroid photos of yourself with your new friends in your travel journal.

2. Start a blog to document your experience

In order to keep all of your friends and family members back home updated on your experience, you may want to consider starting a blog about your experience. Just be sure to post plenty of photos to accompany your posts as your loved ones will be excited to see photos of you living abroad and in the years to come, you’ll also enjoy looking back at your blog posts.

3. Set yourself a weekly budget in order to manage your expenses

in order to avoid running out of disposable cash on your study abroad experience, it’s a great idea to set yourself a weekly budget, which you’ll be able to realistically stick to for the duration of your time abroad. As so many international students waste a large portion of the money which they’ve saved for their trip in their first month abroad.

4. Make sure to have digital copies of all of your important documents

It’s well worth scanning or taking clear smart phone photos of your passport, your student exchange documents and your visas as it always pays to be safe, rather than sorry. Especially, when you’re traveling alone to a foreign country, which you’ve never visited before.

5. Use Skype or Face Time to talk to your loved ones back home

If you ever get homesick, simply video chat with your friends and family members back home, to hear familiar voices without having to pay for expensive international phone calls. Just make sure that you know what time it is in your home city, before calling your loved ones to avoid waking them up in the middle of the night or early in the morning.

6. Take a small trinket with you on your adventure, to remind you of home

Another way to fight homesickness is to pack a small item which reminds you of home, during your study abroad experience. As an example, you may want to pack your favorite mug that your best friend brought you for Christmas or your favorite pillow case or blanket.

7. Join a variety of clubs in order to make new friends

As an example, you may want to join a hiking or skiing club that embarks on regular weekends away.

So if you have your heart set on studying abroad in the future, it’s well worth keeping all the tips listed above in mind.