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Whenever possible, use clear terms to avoid ambiguity. In our example, it’s better to say that the rate changed by 5 percentage points, rather than by 5%. Why do we use percentages? This concept makes calculating simpler when we’re working with parts of 100. Again, it’s easier than basing calculations on thirds, fifths, twelfths or other bases. It’s useful in particular because many fractions do not have a precise non-recurring decimal equivalent. Measuring changes in size: Percentages measure how much a thing changed in size or value relative to how it was before. For instance, an investor’s portfolio may have grown in size by 4% of its original value over the past year. The two circles, together with the line, represent the number 100. By the 1800s, the modern percent symbol dropped the p abbreviation that preceded it. Writers also slanted the line between the two circles. We solve the first-degree equation (the 100 in the denominator passes multiplicatively to the other side): 12 / 80 = x /100 → x = 12 * 100 / 80 → x = 15
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If you think something is wrong or if you would like to add something, open an issue or a pull request! Often, they involve measuring exponential growth or size differences. A 50% growth rate, for instance, indicates that something grows by half its size or value. A rate of 200% shows growth that’s twice the original value, and so on. Long multiplication means you're doing multiplication by hand. The traditional method, or Standard Algorithm, involves multiplying numbers and lining up results according to place value. These are the steps to do long multiplication by hand: Percentages are an important component of analyzing statistical data. These let you show the differences in the subsets of a population with relative ease. They also serve as a template for visual aids. You can use the fraction method above to find the percentage of a subset relative to the population size. This process can be used for any number of fractions. Just multiply the numerators and denominators of each fraction in the problem by the product of the denominators of all the other fractions (not including its own respective denominator) in the problem. EX:You can also use a percentage decrease calculator to see how much an item originally cost if you have the mark-down price (discounted price) if the original price isn’t listed. In this system, even the biggest earners pay the lowest rate on a part of their income. This makes taxation complex, but it has its perks. You don’t need to worry about paying a higher percentage when you get a raise.
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Much like fractions, percentages represent parts of a whole. All percentages are numbers divided by 100. A single percentage point, 1%, is equal to the fraction 1/100. Thus, you can convert them into ratios, decimals, or other fractions. Likewise, you can express any fraction, decimal, or ratio as a percentage. Arrange the numbers one on top of the other and line up the place values in columns. The number with the most digits is usually placed on top as the multiplicand. Next, let’s talk about credit cards. If you have a credit card balance from month to month, you should pay it ASAP. Unlike mortgages and car loans with fixed terms, credit card debt is harder to pay down. Left unpaid too long, this can spiral into toxic debt because of compound interest.
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When multiplying decimals, say, 0.2 0.2 0.2 and 1.25 1.25 1.25, we can begin by forgetting the dots. That means that to find 0.2 × 1.25 0.2 \times 1.25 0.2 × 1.25, we start by finding 2 × 125 2 \times 125 2 × 125, which is 250 250 250. Then we count how many digits to the right of the dots we had in total in the numbers we started with (in this case, it's three: one in 0.2 0.2 0.2 and two in 1.25 1.25 1.25). We then write the dot that many digits from the right in what we obtained. For us, this translates to putting the dot to the left of 2 2 2, which gives 0.250 = 0.25 0.250 = 0.25 0.250 = 0.25 (we write 0 0 0 if we have no number in front of the dot).
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Given how we base percentages on a 100 denominator, it’s understandable why this is confusing. We tend to presume we are starting with the same whole number. When in reality, increasing or decreasing that number has changed the basis for the percentage.
It is forgivable to assume that the percentage sign "%" depicts a fraction. It does look like one at first glance, as does the division symbol, the obelus (÷). You may also question why the symbol has two zeroes in it. After all, isn’t dividing by zero undefined? Some sources claim that the two circles represent a shorthand for one hundred. That, while sort-of true, is not the whole story. The story behind it is much more complex. Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the operation to occur. Refer to the addition section as well as the equations below for clarification. a In the first part, we took 30% of 100. In the second part, we took 30% of 70. Again, the basis for the percentage changes each time you increase or decrease its value. Take note of this to avoid making the same mistake. Working with Populations In its most literal form, percentages mean “part per hundred.” This is the expression of a fraction or ratio where the denominator is 100. The percentage became one of the most popular expressions of fractions for a reason. They illustrate proportion and completeness in a way that’s easy to understand. They also simplify the process of calculating based on a proportion. Percentages convert to decimals, which are much easier to process.
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Other writers sometimes added a line under the p (ꝑ) to show its use as an abbreviation. By the 1600s, the shorthand evolved into a glyph; the c turned into a circle, which rested on top of a line. The o became the bottom circle. Over time, writers began using just the glyph, which resembled an obelus. Incidentally, it was around the same time when the obelus was used as a symbol for division. Of course there are a million and one other reasons why someone would want to figure out percentages, particularly businesses, so these handy online software programs are amazingly time efficient and easy to use. Keeping Up with InflationHere’s another common example. Let’s say you increased a number by 30%, then reduced it by another 30%. You might expect to end up with the same number you started with. But you don’t. This assumption is incorrect. This example shows the practicality of the widespread use of percentages, which is why we need to be able to understand and calculate percentages. The first multiple they all share is 12, so this is the least common multiple. To complete an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value will make the denominators 12, then add the numerators. EX:
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