While scientists need to be able to calculate percentages and probability to do things like determining the specific gravity of an object, almost everyone has to calculate a percentage at some point in the week. Whether you are calculating a tip, doing your taxes, shopping during a sale, or just trying to figure out how likely something is to occur, knowing how to quickly calculate percentages is a valuable skill.
There are different ways to calculate the percentage of different numbers, it just depends on your needs at the moment. Let’s take a closer look at the various ways of calculating percentages.
Convert It Into A Decimal
One of the primary ways of calculating a percentage is to divide one number into the other number, converting it into a percentage. If you’re trying to find out what percentage of 386 the number 239 is, all you need to do is divide 239 by 386. This gives you 0.6191. All you need to do to convert 0.6191 into a percentage is move the decimal over two places to the right. There you have it, it’s 61.9%. This works in reverse too. If you have a percentage that you need to convert to a decimal you can work with, just move the decimal point left two places.
If you have a percentage and need to convert it to a numerical value, you can do this by first converting the percent back into a decimal then multiply the other number by the decimal. Let’s say you’re trying to work out what the interest on a loan would be, and you know that it is 5% of the value. If the initial value of the loan is 1500 dollars and the interest is 5%, start by converting 5% into 0.05. You can now multiply 1500 by 0.05 to get 75. So you know that the total you will owe back is 1575.
What about if you need to determine what unknown number is a specific percentage of another number? Let’s say you’re trying to save 30% out of every paycheck so that you can go on a trip in a couple months. In this case, you’d start by converting the percentage into a decimal. You’d take 0.30 and multiply it by the number you’re attempting to determine the percentage of. If you paycheck for the week was 500, you’d multiply 500 by 0.30. You now know that you’ll need to save 150 out of this paycheck.
If you’re trying to figure out what percentage of change occurred between two numbers, you’ll want to begin by finding the change in value between the two numbers. If the cost of a phone has dropped from 200 to 175, that’s a change of -25 dollars. You would then just take -25 and divide it by 200. This comes out to -0.125, or a decrease of 12.5%.
Iterate On It
If you want a method to reliably calculate percentages in your head, break the problem up into smaller, more manageable chunks:
- If you’re trying to calculate what 15% of 36 is, start by calculating what ten percent of 36 is. 10% of 36 is 3.6. Now you can just take half of 3.6, which is 1.8, and add it to 3.6 to get 5.4.
- Here’s another example. What’s 60% of 48? It’s well known that 50% is just half, so divide 48 in half to get 24. Now take 10% of 48, or 4.8 and add it to 24 to get 28.8.
- Let’s take a look at one more example. How can you get 85% of 72? Since 85% is just 15% less than the whole number, we’ll want to subtract 15% from the number. You can get 7.2 as 10% of 72 and then divide that by 2 to get 5% of 72, 3.6. So just add 3.6 and 7.2 together for a sum of 10.8. Now subtract 10.8 from 72 to get your answer, 61.2 is 85% of 72.
Estimating probability is something people try to do every day, but they often make mistakes while trying to determine probability. Probability can easily be expressed in the form of a percentage, it just requires a little more work to get to that point.
The number of variables you have to take into account will depend on the number of possible outcomes in the event you are observing. Flipping a coin is an example where it’s very easy to calculate the probability. There are only two sides, so there will only ever be half a chance of heads or tails coming up, so a 50% probability of either side coming up. The odds of rolling a specific number on a six-sided die are also fairly easy to calculate. The probability is the same for all six sides.
If you’re trying to figure out the probability that any side would come up when rolling a die, remember that there are six sides and only one “victory” state, or one chance it can come up the way you want it to. Thus there’s a one-in-six chance of it coming up on a specific side. In terms of percentages, you can divide 1 by 6 to get 0.166 or approximately 16.6%.
When it comes to probability, some events are independent while others are dependent. Independent events are those where the outcome of the prior event won’t impact the next event. Dependent events are those where the outcome of the event is impacted by the previous event. Rolling a die is an independent event, as nothing about the property of the die changes when it is rolled. By contrast, drawing a card from a deck of cards, not replacing the card and then drawing another one are dependent events. The probability of drawing the second card is influenced by the fact that you drew the first card and did not replace it.
To determine the percentage probability of an independent event, you just multiply the probability of the various instances together. If you’re trying to figure out the probability of rolling two 5’s on a die in a row, you just multiply ⅙ by ⅙ to get 1/36, or in terms of percentages, that ’s about 2.77%.
In order to figure out the probability of drawing one card after drawing another and not replacing it, remember that there are 52 cards in a deck and the probability goes down by one after you draw one. The probability of drawing a heart from the deck is initially 13/52. After you draw one card it becomes 13/51, assuming the card you drew wasn’t a heart. This means that the probability of drawing a heart on the first two cards drawn from the deck should be 13/52 multiplied by 13/51. This is 169/2652 or about 6.37%.
When calculating percentages, to determine the probability or otherwise, use the method that works best for you. Breaking difficult problems up into smaller chunks is a great way to minimize the difficulty of calculating a percentage.