## Go Figure it Out!

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We use percentages at work in many different ways. We use them to calculate performance against targets and track trends. Percentages help us find profit margins, returns on investment, agency commissions, and mark-ups. We also use percentages to calculate VAT and duty payable.

As consumers, percentages grab our attention when retailers use them in promotions, in store and online. Percentages worry us in news stories about interest rates and inflation rates. They depress us when we find out our kids’ school marks and the percentage of ‘baddie’ ingredients in our food. Doctors like to scare us by telling us our percentage chances of health problems if we do particular things.

**Let’s Get Started!**

You can calculate a percentage in various ways: using a calculator, a phone or computer app or an Excel spreadsheet, or not using a calculator. Either way, first you need to understand the basic sums.

**What is a Percentage?**

A percentage is an amount out of 100 percent. The word ‘percent’ comes from centum, the Latin for a hundred. Instead of writing ‘percent’ in full when we write a percentage figure, usually we use the sign ‘%.’

**How do you Calculate the Percentage of a Number?**

To find the percentage that one number, **X, **is of a second number**, Y,** we divide X by Y to give the quotient, Z.** **You can express the quotient as a fraction or a number with a decimal point. The latter is called the decimal form of the percentage. We multiply the quotient in either form – fraction or decimal – by 100 percent to give the percentage, which we write with a ‘%’ sign next to it.

**What is the Percentage Formula?**

We write the expression ‘number divided by total times 100 percent equals percentage’ as an equation, **x/y x 100% = z %. **This equation is called the percentage formula.

**How do you Calculate a Percentage Increase? **

This calculation involves finding the difference between two numbers, in this case going from a lower number to a higher number, and expressing this figure as a percentage.

Say 90 people viewed your LinkedIn profile last week and 126 viewed it this week. What is the percentage increase? LinkedIn’s algorithms calculate this for us, but for this exercise we’re going to work it out ourselves.

To find the percentage increase, first we find the difference between last week’s total and this week’s total. This is **126 **minus **90**, which comes to **36**. Divide the difference, 36, by the original number, 90. This gives a quotient of +0.4. Multiply this times 100 percent, and you get a percentage increase of +40%.

Another way to work out the percentage increase is to divide the ‘after’ figure by the ‘before’ figure to give the quotient. Then you multiply the quotient by 100%, and then subtract 100% to give the percentage increase.

In our LinkedIn profile scenario, the ‘after’ figure is **126 **divided by the ‘before’ figure **90**, giving a quotient of **+1.4**. Multiply +1.4 by 100% to give **+140%**. Take away 100% and we have a percentage increase of **+40%**.

**How do you Calculate a Percentage Decrease? **

This calculation also involves finding the difference between two numbers and expressing it as a percentage. This time we’re going from a higher number to a lower number.

Suppose 90 people viewed your LinkedIn profile last week but 63 viewed it this week. What is the percentage decrease?

First, we find the difference between last week’s total and this week’s total. This is **90 minus 63**, which is **-27**. Divide the difference, -27, by the original number, 90. This gives a quotient of -0.3. Multiply this times 100 percent, and you get **-30%. **This is the percentage decrease.

**How do I Convert a Decimal to a Percentage?**

You multiply the decimal by 100, which is the same as moving the decimal point two places to the right and add a % sign. So, 0.691 as a percentage is 0.691 x 100%, which is **69.1%.**

**How do I Convert a Percentage to a Decimal?**

Take away the percent sign and divide by 100. This is the same as moving the decimal point two places to the left. So, 69.1% becomes **0.691**.

**How do you Find a Percentage without using a Calculator?**

To find what percentage a number X is of the total Y without using a calculator, we need to express X divided by Y as a fraction. We can write this as** X / Y = Z.**

** **Next, we simplify the fraction to its lowest form. Say we need to calculate 35 as a percentage of 50. Both numbers can be divided by 5, so we can write 35 over 50 as 7/10. We multiply this fraction by 100%. 7/10 is 7 times 10%, which is 70%.

**How do I Work out a Percentage using a Calculator?**

Let’s try an example. What percentage of 60 is 45? As a sum this is 45 divided by 60. Enter the figure 45 on your calculator or the calculator app on your mobile. Press the ‘divided by’ key. Enter the figure 60. Key “=” to give the quotient, or decimal form, as above. 45 divided by 60 gives a quotient of 0.75. Multiply this by 100: press X then enter 100, to give 75. This is the percentage.

**How do you Calculate Percentages in an Excel Spreadsheet?**

If you’re working in an Excel spreadsheet, to find what percentage the value in cell C2 is of the value in cell B2, select cell D2 and enter the formula “= C2/B2.” Working in the Home tab on your spreadsheet, go to the Number box and click on Percentage. This will give your answer as a percentage in cell D2.

** **Here’s an example. Say we have a table with the Customer’s name in the A column, Orders in the B column, and Deliveries in the C column. Smith’s Stores is in cell A2. They have ordered 30 units. This figure appears as 30 in cell B2. 25 units have been delivered so far, represented as 25 in cell C2.

To find the percentage of orders delivered to Smith’s Stores, we select cell D2 and enter the formula “=C2/B2.” Working in the Home tab on our spreadsheet, we go to the Number box and select Percentage. This gives an answer of 83.33% in cell D2.

**Where can I find a Percentage Calculator Online?**

There are various percentage calculators online. Calculatorsoup.com has many different calculators, including one for percentages. You follow the same steps as before. Enter the first figure. Key ‘divided by.’ Enter the second figure. Key “=” to give the quotient, or decimal form, as above. Multiply this figure by 100: press X then enter 100, to give 75. This is the percentage.

Now let’s look at some more uses of percentages in work.

**How do you Work out a Percentage Discount?**

Say I’m giving you £500 off a package that usually sells for £2,000. How much is the percentage discount? £500 divided by £2,000 is 0.25. 0.25 x 100% is 25%. So I’m giving you a 25% discount.

**How do you Calculate a Percentage Mark-up?**

If you buy something for £300 and sell it to your customer for £360, you are marking it up by £60. £60 divided by £300 is 0.2. Multiplied by 100%, this is 20%. So you are making a 20% mark up.

**How do I Calculate Mean as a Percent?**

To calculate the mean percentage of the total for a set of values, first we find the total of all the numbers divided by how many numbers there are. This gives us a mean value. Divide the mean value by the total possible value to give the quotient, and multiply this by 100% to give the mean percentage.

Say 5 salespeople sell 25, 30, 35, 40 and 50 units respectively against an individual target of 50 units. The total sales figure is 180 units. Divide this by the number of salespeople, 5, to give the mean sales value, 36. Divide 36 by 50 to give the quotient, 0.72. We multiply 0.72 by 100% to give the mean percentage the salespeople achieved of the target, which is 72%.

**How do you Calculate the Gross Profit Margin Percentage?**

We calculate the gross profit from the sale, first of all, by working out the revenue from the sale minus the cost of the goods sold. This is the gross profit. Divide the profit by the costs of the goods to give the quotient. Multiply the quotient by 100% to give the gross profit margin percentage.

Say we pay £40 for an item and sell it for £60. The gross profit is £20. Divide the gross profit, £20, by the total revenue, £60, to give the gross profit margin, 0.33. Multiply this by 100% to get the gross profit margin percentage, which is 33 %.

**How do I use Percentages to Calculate VAT?**

To work out a price including the standard rate of VAT, which is 20%, multiply the price excluding VAT by 120%. To work out a price that includes the reduced rate of VAT, which is 5%, multiply the price excluding VAT by 105%.

Removing 20% VAT is a very different calculation. To remove the VAT from a sum, you need to divide the figure by 120%, or 1.2. £100 divided by 1.20 is £83.33. Subtracting £83.33 from £100 comes to £16.67. This gives £16.67 as the VAT on an item sold for £100.

**How do I use Percentages to Calculate APR?**

If you want to borrow money from a bank or finance company, before you sign up with one you need to compare the different lenders. One measure is the Annual Percentage Rate, or APR, the interest rate applied to the principal amount borrowed over a year. The lenders will do the calculations for you when they give you a quote, but it’s good to understand the sums.

To calculate the APR, calculate the interest rate the lenders are offering you. Multiply this by the principal borrowed to give the interest amount. Add the interest to the administrative fees. Divide this combined figure by the loan amount, the principal. Divide this figure by the number of days in the loan term. Multiply the result by 365, for the days in a year. Multiply the resulting figure by 100 to convert to the percentage APR.

Let’s put this as an equation. APR = ((Interest + Fees/Loan amount) / Number of days in loan term)) x 365 x 100%

**How do you Turn Marks into a Percentage Score?**

Knowing what percentage your kids’ marks are out of the possible total is important for parents.

The calculation for marks as a percentage is the same as we’ve been doing to find percentages. Divide the mark scored by the total to give our old mate, the quotient. Multiply the quotient by 100% to give the final percentage.

Now let’s look at some uses of percentages in technology and manufacturing.

**How do People Calculate Percentage Error or Uncertainty?**

The percentage error or uncertainty in a measurement is calculated as the uncertainty or margin for error divided by the measurement, times 100%. So a 2 mm margin of error on a 100 mm measurement is a percentage error of 2%.

**What is a Mass Percentage?**

Mass percentage is a measurement of the concentration of a component in a mixture. The mass percentage is calculated as the mass of the component divided by the total mass of the mixture, times 100%. This is how you work out, for example, the fat content in milk.

**How do you Calculate a Percentage Yield?**

Percentage yield is a very important use of percentages in manufacturing. 100g of calcium carbonate produces 56g of calcium oxide, so 1g of carbonate produces 0.56g of oxide. The quotient is 0.56. Multiplied by 100%, this gives a percentage yield of 56%. We can use this to work out that 250g of calcium carbonate should produce 140g of calcium oxide. But in an industrial process may not be so efficient.

**How Can I Get Better at Percentages?**

Sorry, there’s no shortcut, practice makes perfect. Work at it though and you should reach the point where you can figure out sums in your head, at least roughly, so you can double check your work as you’re going along.

Now, to complete our look at calculating percentages let’s think about using them to work out probability.

**How do you Calculate Percentage Probability?**

When you toss a coin, there are two possible outcomes: heads or tails. One in two is the same as 0.5, so you have a 50:50 chance, or a 50% probability, of throwing heads. Staying with percentage probability, there are six faces on a dice cube. This means you have a one in six chance of throwing a six. 100% divided by 6 gives a percentage probability of 16.6%.

When you go to the races, you can also use percentage calculations to turn fractional odds into percentage probabilities. Say the odds are 5 to 2. That means if your horse wins, for every £2 you bet, you get £5 back. This gives an implied probability of 2 out of 7. Multiplying 2/7 times 100 gives you a 28.6% probability of winning. Good luck!