Converting Fractions to Decimals and Order of Operations

# Converting Fractions to Decimals and Order of Operations -...

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Converting Fractions to Decimals and Order of Operations I. Converting Fractions to Decimals To convert fractions to decimals we just divide. The only catch is when should we stop. Sometimes we end when there is no remainder. Example Convert the fraction 3/8 to a decimal. Solution 0 . 375 8 | 3 . 000 24 60 56 40 40 0 Hence 3 = 0.375 8 Other times the digit repeats itself Example Convert the fraction 5/6 to a decimal. Solution 0 . 833 6 | 5 . 000 48 20 18 20 18 20 We see that if we keep working it out we will continually get 3. That is 5 = 0.833333... 6

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We put a bar over the 3 to indicate that the 3 repeats. 0.83333... = 0.83 Example Convert the fraction 4 2/7 to a decimal. Solution Divide only the fractional part 0 . 285714 7 | 2 . 00000000 14 60 56 40 35 50 49 10 7 30 28 20 We are back to where we began. Hence 2 4 = . 285714 Notice the 4 from the mixed number is the whole number part. 7 Example Fill in the green blank with " < " , " > ", or " = " 2 0.133 15 Solution We first convert the fraction into a decimal. Then compare. We will need to divide until we recognize a difference or recognize equality 0 . 13 15 | 2 . 00 15 50
45 50 We see that this is the repeating decimal 0.13 = 0.133333... Now notice that 0.133 = 0.133000000... < 0.1333333...

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