Decimals
4.1 Order of Operations
 
4.2 Numbers
 
4.3 Factors
 
4.4 Multiples
 
4.5 Fractions
 
4.6 Decimals
 
4.7 Percents
 
 
4.8 Exponents
 
4.9 Roots and Radicals
 
4.10 Scientific Notation
 
4.11 Logarithms
 
4.12 Review Questions
 
4.13 Explanations
 
Decimals
Decimals are just another way to express fractions. After all, to produce a decimal, you simply divide the numerator of a fraction by the denominator. For example, 1/2 = 1 2 = .5.
Comparing Decimals
Like fractions, comparing decimals can be a bit deceptive. As a general rule, when comparing two decimals such as .3 with .003, the decimal with more leading zeroes is the smaller one. But if asked to compare .003 with .0009, you might be tempted to overlook the additional zero, and because 9 is the larger integer, choose .0009 as the larger decimal. That would be wrong. Use caution to avoid such mistakes. It might help to line up the decimal points of the two decimals:
  • .0009 is clearly smaller than .0030
Similarly,
  • .000900 is smaller than .000925
Converting Decimals to Fractions
Knowing how to convert decimals into fractions and fractions into decimals are useful skills. Sometimes you’ll produce a decimal while solving a question, and then you’ll have to choose from fractions for test choices. Other times, it may just be easier to work with fractions. Whatever the case, both conversions can be done easily.
To convert a decimal number to a fraction:
  1. Remove the decimal point and make the decimal number the numerator.
  2. Let the denominator be the number 1 followed by as many zeroes as there are decimal places in the decimal number.
  3. Reduce the fraction.
Let’s convert .3875 into a fraction. First, we eliminate the decimal point and make 3875 the numerator:
Since .3875 has four digits after the decimal point, we put four zeroes in the denominator:
Then, by finding the GCF of 3875 and 10,000, which is 125, we can reduce the fraction:
To convert from fractions back to decimals is a cinch. Simply carry out the necessary division on your calculator, such as for 3/5:
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