In 2017 , the fastest computer in the United States could...

In 2017 , the fastest computer in the United States could handle 17.59 quadrillion calculations per second. (Hint: 1 quadrillion $=1 \times 10^{15}$.) How many calculations could it perform per minute? Per hour? (Data from www.top500.org)

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Key Concepts

Scientific Notation

Scientific notation is a method of expressing very large or very small numbers in the form of a number between 1 and 10 multiplied by a power of ten. It simplifies calculations and comparisons by reducing the number of digits involved and providing a clear structure for multiplication and division, which is especially useful when dealing with quantities like 17.59 quadrillion or 10^15.

Time Conversion

Time conversion involves changing a time measurement from one unit to another, such as converting seconds to minutes or hours. This is done by applying conversion factors, for example, 60 seconds equals 1 minute and 3600 seconds equals 1 hour, ensuring that all calculations are consistent in terms of time units.

Rate Conversion

Rate conversion is the process of adjusting a given rate from one time unit to another. In contexts involving per-second rates, converting to per-minute or per-hour rates requires multiplying by the number of seconds in a minute or an hour respectively. This helps in understanding and comparing speeds of calculations or processes over different periods.

Transcript

00:01 And this problem, we are told that in 2017, the fastest computer can handle is 17 .59 quadrillion calculations per second.

00:11 Now, if you don't know what how many one quadrillion is, you can see using the scientific notation is 1 times 10 to the 15th.

00:19 So when i go to write this number in scientific notation, this little column here is kind of representing what's happening after this one.

00:27 So this is 17 .59 times 10 to the 15.

00:33 So i need to move that decimal point over one more spot.

00:36 I'm going to move it to the left to put it in scientific notation.

00:39 When you move to the left, you're going to add.

00:42 So this becomes times 10 to the 16th.

00:45 So this is what's happening per second.

00:47 And we want to know what is happening per minute.

00:50 So we have to recognize that there are 60 seconds in one minute.

00:53 If i were to write that in scientific notation, it's the same thing as same.

00:57 6 times 10.

00:58 So what i'm going to do is this is what's happening per second.

01:01 I'm going to multiply this now by 6 times 10 to the first power.

01:05 So to begin this next step here, i'm going to multiply 1 .759 times 6 first, and i get 10 .554.

01:15 For the tens, i'm going to add their exponents together because we're using the product rule.

01:20 So 16 plus 1 is 17...

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