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Why cant irrational be represented in decimal form?

A decimal number is eitherterminating,repeating, ornon-terminating and non-repeating.The last of these can never be written out since it has infinitely many digits with no way of abbreviating them. A terminating decimal number is one with at most n digits after the decimal point (where n is finite). Such a number is equivalent to a rational number whose denominator is 10^n. The number is therefore rational.For example, 0.23568 = 23568/100000. It can be simplified but that is not relevant here.A number with a decimal representation with a recurring string of length m (where m is finite) is a rational number whose denominator is a 10^k multiple of 10^m-1 or 99...9 (m times). Here k is related to when the repeating sequence starts.For example, consider 1.23142857142857... (with the 6 digit sequence 142857 repeating)Let f = 1.23142857142857...then 100f = 123.142857142857...and 100f*1000000 = 123142857.142857142857...So that 999999*100f = 123142857-123 which is an integer.f is, therefore a ratio of two integers and so is a rational number.So that only leaves the irrational numbers for infinitely long decimal representations with no recurrence.


What is 0.72 repeating as a fraction?

Turning repeating decimals to fractions are quite simple. All you need to do is take a look at what numbers are being repeated. For this question, as the 7 and the 2 are being repeated, we can see that there are only two numbers being repeated. So we put two 9's as the denominator for the fraction and 72 as the numerator. So a simple way to put this would be, however many numbers that are being repeated, that's how many 9's are needed for the denominator. Therefore, 0.72 repeating is 72/99 and simplified is 8/11.


Related Questions

How many BTUs are required to raise the temperature of 15 pounds of water from 100F to 120F?

To calculate the BTUs required to raise the temperature of water, you can use the formula: BTUs = (pounds of water) x (temperature change in °F) x (1 BTU). For 15 pounds of water going from 100°F to 120°F, the calculation would be: BTUs = 15 pounds x 20°F x 1 BTU = 300 BTUs.


Are cut flowers stronger in cold or warm water?

General opinion is that the correct temperature is 100F


What should the temperature be inside the computer case?

100F/38C Should not exceed 100F/38C


What is the recommended temperature range for tepid water when used for washing hands?

The recommended temperature range for tepid water when used for washing hands is between 60F and 100F.


What is the recommended temperature for a baby's bath water to ensure their safety and comfort?

The recommended temperature for a baby's bath water is around 100F (37.8C) to ensure their safety and comfort.


What is the recommended water temperature for an infant's bath to ensure their safety and comfort?

The recommended water temperature for an infant's bath is around 100F (37.8C) to ensure their safety and comfort.


What is hotter 100f or100c?

100 degrees Celsius is hotter. 100 degrees Celsius is mad temperature for weather and it is the temperature that the water boils.


What is the North Poles average temperature in summer and winter?

100f


What is the temperature range for 5w20 engine oil?

-20F to +100F


What is the recommended water temperature for bathing a baby?

The recommended water temperature for bathing a baby is around 100F (37.8C). It is important to always test the water with your wrist or elbow to ensure it is not too hot before placing the baby in the bath.


What is the recommended water heater temperature for babies to ensure their safety during bath time?

The recommended water heater temperature for babies during bath time is 100F (37.8C) to prevent burns and ensure their safety.


What is the recommended baby water temperature for bathing infants?

The recommended water temperature for bathing infants is around 100F (37.8C). It is important to always test the water with your wrist or elbow to ensure it is not too hot before placing the baby in the bath.