Changing from Fractions to Decimals
Everyone loves fractions. In fact, you probably find it hard to believe that anyone would ever want fractions to change! Okay. I jest. The practical reason for changing from fractions to decimals is to aid in computations and get a sense of the value. It’s easy to trip up when entering a fraction into an arithmetic operation. But decimals work nicely in calculators. Also, the decimal equivalents of many fractions are easier to compare.
Considering the two types of decimals
The two types of decimal numbers that arise from dividing a fraction’s numerator by its denominator are terminating and repeating decimals. A terminating decimal is just what it sounds like: it’s a decimal that comes to an end. You may need to do a bit of dividing to come to that end, but you will find the end. A repeating decimal is one that never ends. Instead, it repeats itself over and over in a distinctive pattern. The pattern may contain one digit, two digits, or a huge number of digits.
Rounding decimals up or down
When rounding decimals, you decide how many decimal places you want in your number, and then you round to the nearer of that place and lop off the rest of the digits. You can also use the Rule of 5 when rounding. I explain the different ways to round in the following sections.
Converting Decimals to Fractions
Decimals have a much better reputation than fractions. Why, for the life of me, I can’t understand. But many people do prefer the decimal point followed by a neat row of digits. For most applications, the decimal form of a number is just fine. For many precision computations, though, the exact form, a number’s fractional value, is necessary. Those working with tools know that fractions describe the different sizes (unless you’re working with the metric system).
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Dealing with repeating decimals
Repeating decimals come from fractions. But unlike terminating decimals, you can’t put the decimal part over the power of 10, because the decimal never ends. In other words, it doesn’t settle down to a particular power of 10, so you’d never stop putting zeros in the fraction.
Percents are found daily in newspaper ads, financial statements, medical reports, and so on. However, the percentages aren’t really the same as the rest of our numbers. You need to change from a percent to a decimal before doing any computations involving percentages of other quantities.
Transforming from percents to decimals
To change a percent to its decimal equivalent, move the decimal point in the percent two places to the left. Moving the decimal point two places to the left gives you the same result as multiplying the percent amount by 0.01 (one hundredth). Why are you multiplying by 0.01? Because percents are comparisons to 100; you’re changing the percent to how many out of 100
Moving from decimals to percent
When you change a number from a decimal to a percent, it’s probably because you have a task in mind. Most likely, you’ve started with a fraction and are using the decimal as the transition number — the number between fractions and percents.
Coming to Grips with Fractions
Fractions are still useful for describing amounts. They’re exact numbers, so a sale proclaiming 1 ⁄3 off the original price tells you to divide by 3 and take one of them away from the original price. Do you get the same thing about changing the fraction to a decimal? No, not really. The decimal for 1 ⁄3 is 0.3333 . . ., which approximates 1 ⁄3 but isn’t exactly the same. You don’t really notice the difference unless you’re dealing with large amounts of money or assets.
To write an improper fraction as a mixed number, you divide the denominator into the numerator. The number of times that the denominator divides is the whole number, in front. The remainder goes in the numerator of the fraction that’s left. If you need to borrow from the whole number in order to subtract, you add the equivalent of 1 to the fraction.
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