Fractions, decimal equivalents

Fourier transforms, A-61 to 64 Fractions, decimal equivalents, A-2 Francium see also Elements... 

Another convenient way to order fractions is to convert the fractions into decimal equivalents and compare. Decimals are reviewed in the forthcoming sections. 

To convert a fraction to a decimal, recall that y means three divided by five. Divide 3 by 5 to get the decimal equivalent of 0.6. To convert a decimal to a fraction, use the place value names for decimals as listed in the sidebar at the start of the decimal section of this chapter. Rewrite the decimal as the named fraction, and then simplify the fraction. For example, 0.018 is read as eighteen thousandths which is Now simplify, t 0q0... 

Memorize some of the common fraction to decimal equivalents. 

Fractions all have decimal values, but some of these decimals terminate (come to an end) and some repeat (never end). As long as the denominator of the fraction is the product of 2s and 5s and nothing else, then the decimal equivalent of the fraction will terminate. To find this terminating decimal, you divide the denominator (bottom) of the fraction into the numerator (top) and keep dividing until there s no remainder. You may have to keep adding 0s in the divisor for a while, but the division will end. 

For example, to find the decimal equivalent for the fraction 7, you divide 25 into 14. To begin the division, you put a decimal point to the right of the 4 and add a 0 to the right of the decimal point. You keep adding Os as needed in the division. This is what I get when I do the division. 

The middle step in changing a fraction to a percent is finding the decimal equivalent (or, in the case of a repeating decimal, the approximate). Table 6-1 shows you some fractions, their decimal value, and then the percent that you get by moving the decimal point two places to the right. 

When you have a percent or fraction that represents a probability, you can use the decimal equivalent of the percent or the fraction to determine a... 

This is a good example of one that does not jump off the page at you. The numbers are definitely not integers neither can they be explained by experimental error. A closer look displays a pattern, however. If you look at the H,. 332 is extremely close to the decimal equivalent of the fraction 4. The 0.167 ending in oxygen is extremely close to the decimal equivalent of the fraction 4 Because 6 is a multiple of 3, the solution appears to require all values to be multiplied by 6. Therefore, the empirical formula for citric acid is ... 

The meaning of afraction such as alb is simply a divided by b. Many fractions therefore have exact decimal equivalents, such as /4 = 0.25 or 1/10 = 0.1. Others do not, such as 1/3 and 22/7, and in many cases we choose to leave these in fractional form to retain their exact values. 

It is important to be able to combine fractions, particularly when they are expressed in symbols or when there is no exact decimal equivalent. 

As Example 2-13 illustrates, sometimes we must convert a fraction to a whole number by multiplication by the correct integer. But we must first recognize which fraction is represented by a nonzero part of a number. The decimal equivalents of the following fractions may be useful. 

Let s look at 25%. Put 25 over 100 to get y y. Notice that reduces to. It is good to be familiar with some of the common fraction and decimal equivalents of percentages. Some are listed in the chart below. 

To order these fractions, it is easiest to find the decimal equivalents. In choice d you have ... 

In mathematics, many difTerent types of numbers can be used. Different situations and settings require different types of numbers. When the number of items in a store display is being counted, the numbers 0,1,2,3, and so on are used. However, to present the batting averages of major league ballplayers, we need fractions and their decimal equivalents. For example, if a player has 136 hits in 418 at bats, his average is =. 325. 

Decimal Equivalent (to two places) Fraction To convert to integer, multiply by... 

Miscellaneous Mathematical Constants Decimal Equivalents of Common Fractions Quadratic Formula... 

Decimal equivalents of common fractions, A-2 Decinormal solutions... 

A-6 Altitude and Atmospheric Pressures, 578 A-7 Vapor Pressure Curves, 579 A-8 Pressure Conversion Chart, 580 A-9 Vacuum Conversion, 581 A-10 Decimal and Millimeter Equivalents of Fractions, 582 A-11 Particle Size Measurement, 582 . A-12 Viscosity Conversions, 583 A-13 Viscosity Conversion, 584 A-14 Commercial Wrought Steel Pipe Data, 585 A-15 ... 

To convert the percentage of a number to equivalent decimal fraction, first drop the percent sign and then divide the numerator by 100. 

The decimal system is a way to name numbers based on the powers of 10. The numbers to the right of the decimal point are fractional equivalents with denominators that are powers of ten. 

To change a terminating decimal to its fractional equivalent, create a fraction that has all the digits to the right of the decimal point in the numerator and, in the denominator, a power of 10 that has as many zeros as there are digits in the numerator. Then reduce the fraction. For the decimal 0.1875, you write 1875 in the numerator and a 1 followed by four zeroes in the denominator. 

The usual move from fractions to percents is through decimals — the decimal format is the middleman in the process. You probably already know some of the more common equivalences of percents and fractions. You know that 50 percent is equivalent to Vi and 25 percent is equivalent to A. Well, I m assuming that you know this, but, just in case, here are some properties and techniques that you can use to make the transitions easier. You don t have to memorize these properties, but having some of them in mind as you re working on percentage problems is helpful. 

For example, 45 percent has a decimal value of 0.45, and the fraction equivalent is Another example is 0.032 percent, which has a decimal... 

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