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There are certain shortcuts, but here is the general idea. For example, convert 0.4121212... to a fraction. Call this number "x", and write:
x = 0.4121212...
Multiply this equation by 100, in this case, because two digits repeat; if three digits repeat, multiply by 1000, etc. Write the equations one below the other, as follows:
100x = 41.21212...
x = 0.4121212...
Now subtract one equation from the other:
99x = 40.8
Solve for x:
x = 40.8 / 99 = 408 / 990
Simplify the answer.
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Is a repeating decimal rational?
yes, repeating decimals (those that have infinite - never ending - number of digits after the decimal point and these decimals show repeating pattern) are rational numbers, because they can be written as fractions.
How do you turn fractions into decimals and example?
To turn improper and proper fractions to decimals, divide the numerator by the denominator. Examples: 1. 27/10 = 27 ÷ 10 = 2.7 2. 11/36 = 11 ÷ 36 = 0.3055 To turn mixed fractions to decimals, add the whole number to the quotient of the proper fraction. 6 1/8 = 6 + (1 ÷ 8) = 6 + 0.125 = 6.125
Is a rational number a repeating decimal?
All repeating decimals are rational numbers. Not all rational numbers are repeating decimals.
What are two characteristics of a rational and irrational number?
Rational numbers - can be expressed as a fraction, and can be terminating and repeating decimals. Irrational numbers - can't be turned into fractions, and are non-repeating and non-terminating. (like pi)
Can all terminating decimals be written as fractions?
All terminating decimals can be written as fractions.
Why are repeating decimals changed to fractions?
There are times when working with fractions is more convenient than working with decimals.
Is 0.16 repeating irrational?
No, no repeating decimal is irrational. All repeating decimals can be converted to fractions. They are, however, non-terminating.
How do you add repeating decimals?
Convert the repeating decimals into fractions, and then add those. If you need it as a decimal, then you can just convert the product back into a decimal!:)
Real life situation for changing repeating decimals into fractions?
there are None!
What is the relationship between repeating decimals and fractions?
They are both representations of rational numbers.
What can rational numbers be expressed as?
fractions or decimals
Why are repeating decimals common to get after dividing?
all rational fractions are repeating. When you divide, eventually the remainder will repeat and then will the sequence
How do you turn decimals into ratios?
Convert them to fractions.
Is a repeating decimal rational?
yes, repeating decimals (those that have infinite - never ending - number of digits after the decimal point and these decimals show repeating pattern) are rational numbers, because they can be written as fractions.
Is 3.25 repeating an integer?
No because integers are whole numbers without decimals or fractions.
How can a decimal change to a repeating fraction?
Fractions don't repeat, decimals do. 4/9 = 4 divided by 9 = 0.4444 repeating
What is it called when fractions terminating repeating decimals integers and percents called?
They are called rational numbers
