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How does 1 over 3 to 100th power have a repeating or terminating decimal representation?
It is repeating. Any fraction in simplest terms which has ANY prime factor other than 2 or 5 in its denominator will be a repeating fraction.
What causes the difference in terminating decimals and repeating decimals?
If a fraction is a rational number then if the denominator goes into the numerator or into the numerator multiplied by a power of 10, then you will have a terminating decimal. Otherwise it will be a repeating decimal.
Why do you multiplied by a power of 10 when writing a repeating decimal as a rational number?
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.
Is the fraction 7 over 6 a terminating decimal or a repeating decimal?
Well honey, let me break it down for you. The fraction 7/6 is an improper fraction, meaning the numerator is greater than the denominator. When you divide 7 by 6, you get 1 with a remainder of 1. So, it's not a terminating decimal, nor is it a repeating decimal. It's just a sassy little fraction that doesn't conform to your decimal rules.
How can you use place value to write a terminating decimal as a fraction with a power of ten in the deminator?
Finding a place value in a terminating decimal is easy. When placing the decimal always remember to place it at the tenth.
What is 0.966129 raised to the 100th power?
0.966129100 = 0.0319 (answer accurate to 4 decimal places only)
Why do I get a repeating decimal when I divide?
When you get a repeating decimal when dividing, it means that the decimal representation of the quotient has a repeating pattern of digits. This occurs when the divisor (the number you're dividing by) is not a factor of 10, leading to a situation where the division process does not result in a clean, terminating decimal. The repeating decimal is a way to represent the fraction that results from the division in a concise form.
Why are number 4 a terminating decimal?
Because 4 is a factor of a power of 10: 4 divides into 100.
What is negative 6.8 repeating decimal as a fraction?
To convert a repeating decimal to a fraction, let x = -6.8. Multiply the repeating decimal by a power of 10 to eliminate the repeating part. Therefore, 10x = -68.8888.... Subtract the original equation from this to get 9x = -75, which simplifies to x = -75/9. Thus, the fraction form of -6.8 repeating decimal is -75/9.
How do I multiply a fraction to a 100th power?
You can either calculate the fraction and raise the result to the 100th power or raise the numerator to the 100th power and divide it by the denominator raised to the 100th power.
is 1.0227 a rational number?
Rational numbers are any numbers that are Terminating and Not repeating Terminating meaning a decimal that simply has an end, repeating decimals while still having an infinite amount of digits can actually be simplified to a fraction. Therefore 1.0227 IS Rational But for example, 0.888888888888... isn't terminating, but it IS repeating since there is a predictable sequence of numbers. For this simple repeating decimal we can just use the nine's trick and say that 0.8 repeating is equal to 8/9 But to solve it we first have to fit this number into a writable variable, so let's say that X = 0.8 R (Repeating) so now we have to add a power to 10 for each number in the pattern/sequence that is repeating and multiply 0.8 R and the value of X by it, so in this case (0.8) there is only one number in this sequence, therefore we would do, 10X = 100.88 R (an asterisk or * means multiplication) Which is, 10x = 8.88 R Therefore we take each side of the expression and subtract the value of X (Which is still 0.8 R) from them. So, 10x - x = 9x (since ten 0.8's minus one is nine 0.8's) and, 8.88 R - X (0.88) is 8 (since X cancels out the infinity of eights, leaving you with a difference of 8) Which in conclusion means 9x = 8 So X = 8/9 (eight ninths, or eight over nine) Hope this was useful :)
How can you predict whether a fraction will give a recurring or terminating decimal?
Reduce the fraction to its simplest form - that is, remove any common factors between the numerator and denominator. If the denominator now is a factor of some power of 10, that is, if the denominator is of the form 2a*5b then the fraction will me a terminating decimal. If not, it will not.
