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Category Archives: Decimals

Decimals to Fraction!

In math there are many things that go hand in hand, for example addition and subtraction, also multiplication and division. Another thing that goes hand in hand is fractions and decimals. We can take a fraction and make it decimal but we can also have a decimal and make it into a fraction. In order to do so we need to understand the term “rational numbers”. Rational numbers are simply decimals that are terminating or repeating.

We can take the word “rational” we can take out the word “Ratio” meaning of integers (fraction of integers).

Terminating decimals are numbers like 0.55, 0.205, and 6.1 (these are all decimals that have a clear ending). We can make these decimal into fractions by paying attention to the place values that the digits hold. For example 0.55 is in the hundredths place therefore 0.55 is 55/100.

Repeating Decimal are numbers like 0.333333….., 0.77777….,and 0.242424 (decimals that have a repetition in the number. it may start later in the number). We can make these decimals in to numbers by setting them equal to “X”. A good example is 0.333333…. because we know of the top of our heads that it is 1/3 but do we know why it is? Below are the steps to show why 0.3333…. is 1/3.

Step 1)     X=0.333333…. 

Step 2) 10X=3.333333…. (Find a number of ten that will get rid of the repeating end of the decimal. Then subtract Step 1 and Step 2.)

Step 3) 9X=3

Step 4) 9X/9=3/9 or 1/3

We can use these steps on any repeating decimals. Lets try the decimal 0.242424….! We will start the problem just like we did for 0.333……!

Step 1) X = 0.242424

Step 2) 100x = 24.2424    (We want to set it equal to 100X because it will move the decimal two places to the right and it will get rid of the repetition)

Step 3) 99X = 24

Step 4) 99X/99 = 24/99 or 8/33

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Posted by on November 3, 2011 in Decimals

 

Decimals….

First we need to know the terminology for decimals before we jump in, the terminology is very important. We can start off by understanding the meaning of the Latin word decem, which mean ten. Some of the other terms that we need to understand are decimal points, and mixed decimals.

The Decimal point is the dot between the digits in a number. For example 17.63 the dot between the 17 and the 63 is the decimal point. 17.63 can also be considered a mixed decimal! Another important thing to pay attention to is the place values when dealing with decimals.

Above is a picture with Place Values for numbers with decimals. On the Left side of the decimal we can see that the ending is “s” and that on the right side the ending are “ths”. These are very important to pay attention too.

We can also write the number in an extended form.

5(10^3)+ 4(10^2)+ 7(10)+3(1)+ 2(1/10) +8(1/100) +6(1/1000)

When we read the number we read it in a different way than what we would if just reading a whole number. When reading a decimal we say the word “and” when we come across the decimal. Below is a example of this.

 
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Posted by on November 2, 2011 in Decimals