Doing Fractional Exponents on Basic Scientific Calculator

In summary, to calculate 8-1/3 on a regular scientific calculator, you can use logs or enter "1/2" directly. Using logs, you would enter -log(8)/3 to get the precise value. However, it is best to consult the user's manual as different calculators may have different methods of input.
  • #1
bballwaterboy
85
3
Suppose you have 8-1/3 and want a precise value for it. How would you go about calculating this on a regular scientific calculator.

I punched in:

8, then the exponent button, then 1, then negative, then division, and finally 3. The calculator reads "error."
 
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  • #2
Use -0.33333... with as many digits as your calculator accepts. The error will be comparable to usual rounding errors, and the calculator would not calculate it more precisely even if you find a way to enter "-1/3".
 
  • #3
bballwaterboy said:
Suppose you have 8-1/3 and want a precise value for it. How would you go about calculating this on a regular scientific calculator.

I punched in:

8, then the exponent button, then 1, then negative, then division, and finally 3. The calculator reads "error."
It's not clear what a 'regular scientific calculator' means. Some calculators use algebraic entry; some use reverse Polish notation (primarily the HP brand).

This is a question which is best left up to the user's manual.

In any calculator, you can always use logs to calculate 8-1/3.

log (8-1/3)) = -(1/3) log (8) = -log (8) / 3. The answer is then 10-log(8)/3

You can also use natural logs and ex to convert the natural log back into a number.
 
  • #4
Or you could just enter "1/2" to begin with!
 
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Related to Doing Fractional Exponents on Basic Scientific Calculator

What is a fractional exponent?

A fractional exponent is a way to represent a power that is not a whole number. It is written in the form of a fraction, where the numerator is the power and the denominator is the root. For example, 2^(1/2) represents the square root of 2.

How do I do fractional exponents on a basic scientific calculator?

To do fractional exponents on a basic scientific calculator, use the "^" or "x^y" button. Enter the base number, then press the "^" button, followed by the numerator of the fractional exponent. Then press the "/" button, followed by the denominator of the fractional exponent. Finally, press the "=" button to get the result.

Can I use negative numbers as the base or exponent in fractional exponents?

Yes, you can use negative numbers as the base or exponent in fractional exponents. Just be sure to enclose the negative number in parentheses before entering the fractional exponent. For example, (-2)^(1/3) represents the cubed root of -2.

What is the difference between a fractional exponent and a radical?

A fractional exponent and a radical both represent roots, but they are written differently. A fractional exponent is written as a power with a fraction, while a radical is written as a symbol (√) with a number inside. They both represent the same operation, so you can convert between them by using the power and root buttons on your calculator.

Can I use fractional exponents to solve equations?

Yes, fractional exponents can be used to solve equations. They can be used to simplify expressions and solve for unknown variables. Just like with regular exponents, you can use the properties of exponents to manipulate equations with fractional exponents.

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