Video: Calculating the Order of Magnitude of a Value

Determine how many floating-point operations a supercomputer can perform in a human lifetime. Use a value of 10⁻¹⁷ s as the time for a single floating-point operation in a supercomputer and a value of 10⁹ s for a human lifetime.

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Video Transcript

Determine how many floating-point operations a supercomputer can perform in a human lifetime. Use a value of 10 to the negative 17th seconds as the time for a single floating-point operation in a supercomputer and a value of 10 to the ninth seconds for a human lifetime.

Let’s highlight the vital information given to us in this statement. We’re told that every single floating-point operation takes 10 to the negative 17th seconds to execute and that the length of a human lifetime is 10 to the ninth seconds. We want to divide these numbers one into the other. Since we’re after the number of floating-point operations computable in a human lifetime, we’ll divide 10 to the ninth by 10 to the negative 17th. When we divide exponents like this, we recall the rule that 10 raised to the 𝐴 power divided by 10 raised to the 𝐵 power is equal to 10 to the 𝐴 minus 𝐵 power.

So in our case, this fraction equals 10 to the ninth minus negative 17 which equals 10 to the ninth plus 17 or 10 to the 26th. That’s equal to the number of floating-point operations the supercomputer can perform in a human lifetime.

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