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When you write a repeating decimal into a fraction why does the fraction always have only 9s or 9s and 0s as digits in the denominator?
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When you divide the numerator of a fraction by the denominator you always get a decimal that ends?
Not necessarily.
Is any factor of 3 or 9 as a denominator always to be a repeating decimal?
No. 36/9 = 4
Can fractions always be written as decimals?
You can always convert a fraction to a decimal. For some fractions, you'll get terminating decimals. For example, 1/8 = 0.125. For other fractions, you get repeating decimals, such as 1/7 = 0.142857 142857 142857...To convert the fraction to a decimal, just divide the numerator by the denominator, for example on a calculator.
Why does 39 divided by 99 equal 0.39393939 repeating?
Simply because the solution to your sum produces a repeating decimal. Just as 22/7 (The value of Pi as a fraction) produces the repeating decimal 3.142857
What does four ninths mean in a terminating or repeating decimal?
It does not mean anything except that it is called a 'Vulgar (or common) Fraction'. It can be mathematically converted into a Decimal Fraction by dividing the numerator , by the denominator. EG. 4 divided by 9 = 0.44444 repeating. It simply means that it it is an Indeterminate quantity and no matter how many times you keep dividing it, there will always be a remainder. It is quite OK to say that 4/9 = 0.4 repeating. You don't have to use more than 1 figure 4 after the decimal point because they will all repeat the same as the first number after the point.
When writing a repeating decimal as fraction why does the fraction always have only 9s as the denominator?
There can be no answer to the question because it is based on a false assumption.0.3333... repeating = 1/3 : I don't see any 9s in the denominator!or 0.0111... repeating = 11/990 : I would not consider the last digit in the denominator to be 9.Having said that, the significance of 9 is that we count in blocks of one more: 10s.
When you divide the numerator of a fraction by the denominator you always get a decimal that ends?
Not necessarily.
Is any factor of 3 or 9 as a denominator always to be a repeating decimal?
No. 36/9 = 4
Can fractions always be written as decimals?
You can always convert a fraction to a decimal. For some fractions, you'll get terminating decimals. For example, 1/8 = 0.125. For other fractions, you get repeating decimals, such as 1/7 = 0.142857 142857 142857...To convert the fraction to a decimal, just divide the numerator by the denominator, for example on a calculator.
When you divide the numerator of a fraction by the denominator you always get a decimal that ends a terminal decimal?
Not at all. The quotient of 1/3 doesn't end.
A repeating decimal is an irrational number?
Not always because any decimal that can be expressed as a fraction is a rational number as for example 0.33333.....repeating can be expressed as 1/3 which is a rational number
Why does 39 divided by 99 equal 0.39393939 repeating?
Simply because the solution to your sum produces a repeating decimal. Just as 22/7 (The value of Pi as a fraction) produces the repeating decimal 3.142857
What does four ninths mean in a terminating or repeating decimal?
It does not mean anything except that it is called a 'Vulgar (or common) Fraction'. It can be mathematically converted into a Decimal Fraction by dividing the numerator , by the denominator. EG. 4 divided by 9 = 0.44444 repeating. It simply means that it it is an Indeterminate quantity and no matter how many times you keep dividing it, there will always be a remainder. It is quite OK to say that 4/9 = 0.4 repeating. You don't have to use more than 1 figure 4 after the decimal point because they will all repeat the same as the first number after the point.
A decimal such as 0.111 is a what decimal?
A fraction that repeats continuously without stopping is called a recurring fraction. 0.1 recurring, or 0.111111... is equal to 1/9, or one ninth.A fraction with a prime denominator other than 2 or 5, always produces a recurring decimal.
Is a repeating decimal a rational number?
Always
How do you turn a decimal into a fraction using the calculator?
Read the whole thing through first to make any sense. I hope it helps you. If the decimal is non-repeating: divide the number over 100. Ex. 0.5= 50/100= 1/2= 0.5, .25= 25/100= 1/4= 0.25, .375= 375/1000= 3/8= 0.375 always have at least two numbers over 100, 0.5= 50/100, and have the same number of digits as the decimal, .375=375, but it has to be over 1000 because there has to be one more digit on the bottom number (denominator) than the top number (numerator). If the decimal is repeating: divide the number over 99. Ex. 0.3 repeating= 33/99= 1/3= 0.3 repeating, 0.45 repeating= 45/99= 5/11= 0.45 repeating, 0.142857 repeating= 142857/999999= 1/7= 0.142857 repeating. always have at least two numbers over 99, 0.3= 33/99, and have the same number of digits as the decimal, 142857/999999, but it has to be over 999999 (6 9's) because there has to be the same number of digits on the bottom number (denominator) and on the top number (numerator). The two options I have explained only work to a certain extent. A regular calculator will not convert a decimal to a fraction. You will have to work it out by hand from the two ways I have explained. If you have a TI-34 II and maybe only some other certain calculators, type the decimal in and type the fraction button, and it will tell you the fraction in lowest terms.
Is a repeating decimal sometimes a rational number?
Repeating decimals are always rational.
