Monday, October 14, 2013

Converting Fractions to Decimals

In class we talked about three different strategies you can use to convert fractions into decimals.  It is my recommendation that you start with the easier strategies and work your way down.  When looking at a fraction to convert to a decimal first think about those benchmark fractions we talked about in class.  Hopefully you have memorized some and have noticed the patterns they create.  This will help you convert the fraction quickly.

 Fraction Benchmark Decimal Benchmark Pattern 1/2 .5 1/4, 2/4, 3/4 .25, .5, .75 +0.25 1/8, 2/8, 3/8, 4/8, 5/8, 6/8,7/8 0.125, 0.25, 0.375, 0.5, 0.625... +0.125 1/16, 3/16, 5/16…. 0.0625, 0.125, 0.1875... +0.0625 1/3, 2/3 .333..., 0.6666... +0.3 (repeated) 1/6, 2/6, 3/6, 4/6, 5/6 0.166.., 0.33..., 0.5, 0.66..., 0.833.. +0.166... 1/9, 2/9, 3/9, 4/9, 5/9…. 0.111..., 0.222...0.3333, 0.444 +0.1 (repeated) 1/5, 2/5, 3/5, 4/5 0.2, 0.4, 0.6, 0.8 +0.2 1/10, 2/10, 3/10, 4/10, 5/10, 6/10... 0.1, 0.2, 0.3 +0.1
If you can not remember the benchmarks or one does not exist, look to see if you can find a common denominator with a base ten number.  This works because our decimal system place values uses base ten numbers like, tenths, hundredths, thousandths and so on.

 Fractions Decimals Strategy ¼, ¾, ⅕ , ⅓, 7/10 See Above Benchmark 12/16, 15/45, 21/30 0.75, 0.333..., 0.7 Reduce the fraction firstthen use Benchmark 14/25, 23/50, 19/20 0.56, 046, 0.95 All of the denominators are factors of100.  Use equivalent fractions to determine decimal 4/125, 7/250 0.032, 0.028 Both denominators are factors of 1000
If all else fails the final strategy is a way to convert any fraction to a decimal.  You need to use the traditional division algorithm.  Sometimes these problems do not work out nicely and the decimal continues on.  I have asked you to round to the nearest hundredth in this case.  This means you need to divide up to the thousandths place to be able to round the hundredths.

Converting Fractions Using Long Division

Some fractions are more difficult to convert into decimals because either they do not have an easy benchmark to remember or do not into a base ten denominator easily.  Therefore, the only way to convert is to divide the denominator into the numerator to get the decimal value of the fraction.  This method will work for any fraction.

Steps
1.  Your denominator is your divisor (the number that is doing the dividing) and your numerator is the dividend (the number that is being broken apart.  Set up your problem like this.  The image is a bit misleading. Notice that a decimal point and zeros should be added to the dividend since it is smaller than the divisor.  This allows you to compute.

2. Divide.  The following fraction works out evenly.  Many times this does not happen.  If that is the case be sure to read the directions on your assignment. Usually the directions will ask you to round to the nearest hundredth.  If there are no directions, it is safe to assume to round to the nearest hundredth.  This means you need to divide up to the thousandths place to determine whether you round up or not.