Multiplying by ten to the power k moves the decimal point k places to the right. If the repeating sequence comprises n digits and you multiply by 10n then the decimal point is moved n places to the right and the positions of the repeating sequence relative to the decimal point is not changed. This allows you to subtract the one repeating decimal expression from the other and get a terminating decimal which can then be used as the numerator of the ratio.
You know a decimal is repeating when you keep getting the same remainder and you keep adding the same decimal onto the end. On calculators it may be expressed as, as an example, 0.6666667. When writing a reoccurring (repeating) decimal it is usually expressed as one decimal with a line over the top of it.
0.12 IS an ordinary number. It is an ordinary rational number, written in decimal form - which is a perfectly ordinary way of writing numbers.
One third of a ton=666.67lbs.
3.7854
1,000,000,000 = 1 x 109 The rules of writing a number in this scientific notation are : M x 10N , where M is a rational decimal number between 0 and 10 and N is the Power of Ten it is raised to.
Yes, of course. Different denominators in the rational equivalent give rise to different lengths of repeating strings.
it is irrational because you just keep writing the same number over and over again!
No... you can write it to any number of decimal places.
0.1714285714285714285714 etc.. And although it does turn out to be like that, the proper way to right it without repeating is .....________ 0.1714285 Note: Please ignore the dots in front of the line. And the line is to be writing above the number starting with the 7, indicating that that's what repeats. Also keep in mind that just because that it's a repeating decimal doesn't mean it's irrational. It's written as a fraction. Any fraction is rational, so this repeating decimal is rational.
You know a decimal is repeating when you keep getting the same remainder and you keep adding the same decimal onto the end. On calculators it may be expressed as, as an example, 0.6666667. When writing a reoccurring (repeating) decimal it is usually expressed as one decimal with a line over the top of it.
1. As a decimal value, write: .3 (with a horizontal line above the 3 or by writing (repeating)) 2. As a percentage, write: 33.3% or 33.3 percent (with a horizontal line above the 3 that is to the right of the decimal point or by writing (repeating))
10.59 repeating. Other than that, 10.6 is the only way of writing 10.6 in decimal notation.
0.12 IS an ordinary number. It is an ordinary rational number, written in decimal form - which is a perfectly ordinary way of writing numbers.
Any terminating or non-terminating decimal digit is rational. The easiest way to look at this is, writing the number in the fractional from. 0.18 can be written as 18/100. Now, by the definition of a rational from, 18/100 is of the standard "p/q" from where q is not equal to 0 (q=100 here). Thus, it is a rational number.
You tell us. Is that all there is to it ? Did you write the whole thing, or does it repeat ? If you stopped writing because you came to the end and there wasn't any more, then it sure looks as if it terminated, doesn't it.
If it can be expressed as a fraction then it is a rational number
No because it can be expressed as a fraction and so therefore it is a rational number