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How Does 1 over 2 to 100th power have a repeating or terminating decimal?
Wiki User
∙ 6y ago
It has a terminating decimal.
Wiki User
∙ 6y ago
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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.
Is the fraction 7 over 6 a terminating decimal or a repeating decimal?
It is a recurring decimal. You only get a terminating decimal if, in the lowest form, the denominaor of the fraction is a factor of 10 or a power of 10. That is to say, only if the denominator is of the form 2m5n where m and n are non-negative integers.
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.
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 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 do you change terminating but reapeating decimal to fraction?
First of all, this question is not clear. How can you have a terminating but repeating fraction? Unless you mean a fraction like 0.234234 that ends but has a pattern. In that case, see Scenario 1.Scenario 1For terminating decimals, simply rewrite the decimal as a fraction with a denominator of a multiple of ten (for example, 0.313 => 313/1000) and simplify it as much as possible.Scenario 2For repeating decimals, the process is a lot more complicated.First, figure out the pattern in the repeating decimal. Then write only the first part of the decimal with at least two repetitions of the pattern (for example, 0.123123...) and place ... to signify that the pattern continues.I will use the decimal number 0.123123... as an example.Then make one "chunk" of the pattern appear before the decimal point, as in 123.123... Note what power of ten you used to make the decimal number into the number with the "chunk" before the point. In this example it is 1,000 (0.123123... x 1000 = 123.123...)Then write that power of ten before n, the fraction you are solving for, and then just plain n with its value:1000n = 123.123...n = 0.123123...Then subtract the values. The answer in this case is 999n = 122.Then get n alone (in this example, divide both sides by 99) and you're all set!
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.
