Mathematics

How Decimals indicate Fractions



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A fraction is a ratio between two integers and also represents division. The top number of a fraction is called the numerator and the bottom number is called the denominator. The fraction 2/10 is read as 2 tenths and is the same as taking 2 and dividing by 10. To convert the fraction to a decimal, use long division and you'll see the answer is .2 .


The first number after the decimal point is the tenths digit, the second is the hundredths digit, the third is the thousandths digit and so on. So when seeing a decimal such as .2 you know right away that is 2 tenths and as a fraction that is 2/10. If the decimal was .22, that is 22 hundredths, which is 22/100. To simplify the fraction, divide that numerator and denominator by 2, to get 11/50. If the decimal is .222, that is 222 thousandths, which is 222/1000, simplified by dividing by 2 to get 111/500.


One can understand decimal conversion to fractions by thinking of real life situations. If you are at a store and see a price of $0.25, everyone knows that is 25 cents, so you can pay with a quarter.. A quarter is a quarter of a dollar and a quarter written as a fraction is 1/4, 1 part out of 4. For $0.01, that is 1 cent and we know that 100 cents equals a dollar, so the fraction is 1/100. For a value over a dollar, such as $1.25 you can think of the number to the left of the decimal as the whole and convert the numbers to the right of the decimal into a fraction.


So 1 is the whole, .25 is the decimal. That converts to 1 25/100, which is 1 1/4. In some cases it's better to change a decimal into a fraction, those cases are repeating decimals. One such decimal is .3333 repeating. Instead of writing .3333 repeating, change it to 1/3. Again you can tell that .3333 repeating is 1/3 by dividing 1 by 3, either by hand or by calculator. Sometimes information will be represented by percentages, which can be converted to decimals and then to a fraction. For example, 35% is the same as .35 as a decimal and 35/100 as a fraction, simplified to 7/20. The conversion from percentage to decimal is simple.


Move the decimal point 2 places to the left. 45% is .45, 125% is 1.25, 1% is .01, and so on. Decimals, percents and fractions are all interrelated and basically the same thing represented in different ways.

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