Algebra I All-in-One For Dummies. Mary Jane Sterling

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Changing Fractions to Decimals and Vice Versa

      Decimals are nothing more than glorified fractions. Decimals are special because, when written as fractions, their denominators are always powers of 10 — for example, 10, 100, 1,000, and so on. Because decimals are such special fractions, you don’t even have to bother with the denominator part. Just write the numerator and use a decimal point to indicate that it’s really a fraction with a denominator that’s a power of 10.

The number of digits (decimal places) to the right of the decimal point in a number tells you the number of zeros in the power of 10 that is written in the denominator of the corresponding fraction.

      Here are some examples of changing decimals to fractions:

      

Q. Change 0.408 to a fraction.

      A. . The decimal has three digits, 408, to the right of the decimal point, so you use the power of 10 with three zeros.

      Q. Change 60.00009 to a fraction.

      A. . The decimal has five digits, 00009, to the right of the decimal point, so you’ll need 100,000 in the denominator. The 60 is written in front of the fraction and doesn’t affect the decimal value. The lead zeros are not written in front of the 9 in the numerator of the fraction. You start by writing the first nonzero digit.

      

A digit is any single number from 0 through 9. (But, when you count the ten digits at the end of your feet, you start with 1 and end with 10.)

      Decimal fractions are great because you can add, subtract, multiply, and divide them so easily. The ease in computation (and typing) is why changing a fraction to a decimal is often desirable.

      Making fractions become decimals

      All fractions can be changed to decimals. In Chapter 1, you are told that rational numbers have decimals that can be written exactly as fractions. The decimal forms of rational numbers either end (terminate) or repeat in a pattern.

      To change a fraction to a decimal, just divide the top by the bottom.

      

Q. Write as a decimal.

      A. becomes and so .

      Q. Write as a decimal.

      A. becomes and so . The division never ends, so the three dots (ellipses) tell you that the pattern repeats forever.

If the division doesn’t come out evenly, you can either show the repeating digits or stop after a certain number of decimal places and round off. Another way to show repeating digits is to draw a bar over the digits that repeat. So can be written as .

      Rounding decimals

      To round a number means to create an approximate value. If you’re measuring the distance from one side of the street to the other and have a measurement of 37 feet, inches, you probably don’t need a number that precise. Depending on what you’re doing, you may be fine with 37 feet — which is the number rounded to the nearest foot. Or 37 feet 3 inches may do it for you. It just depends on the circumstances.

      To round decimal numbers:

      1 Determine the number of places you want and look one further to the right.

      2 Increase the last place you want by one number if the one further is 5 or bigger.

      3 Leave the last place you want as it is, if the one further is less than 5.

      The symbol ≈ means approximately equal or about equal. This symbol is useful when you’re rounding a number.

      Here are some examples of rounding each decimal to the nearer thousandth (three decimal places):

      

Q. Round 0.363636 to the nearest thousandth.

      A. 0.364. When rounded to three decimal places, you look at the fourth digit (one further). The fourth digit is 6, which is greater than 5, so you increase the third digit by 1, making the 3 a 4.

      Q. Round 0.03125 to the nearest thousandth.

      A. 0.031. When rounded to three decimal places, you look at the fourth digit. The fourth digit is 2, which is smaller than 5, so you leave the third digit as it is.

      Writing decimals as equivalent fractions

      Decimals representing rational numbers come in two varieties: terminating decimals and repeating decimals. When changing from decimals to fractions, you put the digits in the decimal over some other digits and reduce the fraction.

      Getting terminal results with terminating decimals

      To change a terminating decimal into a fraction, put the digits to the right of the decimal

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