Perplex
Dashboard
Learn

No active concepts yet.

Browse by TopicReview VideosFormula BookletMy Progress
BlogLanding Page
Sign UpLogin
Perplex
Perplex
Dashboard
Learn

No active concepts yet.

Browse by TopicReview VideosFormula BookletMy Progress
BlogLanding Page
Sign UpLogin
Perplex

Approximations & Error (Lesson 3/3)

Error

1 / 12

Discussion

We saw in the rounding numbers section that the level of precision available when measuring values can impact the final answer of a calculation. Finding the volume of water in a graduated cylinder with markings every ​1​ ​mL,​ for example, could result in a different answer than finding the volume of the same amount of water in a different graduated cylinder that has markings every ​0.25​ ​mL.

Both of these cylinders have the same amount of water in them, but if we took the measurement using the first cylinder we'd get ​25​ ​mL,​ and if we took it using the second, we'd get ​25.25​ ​mL.

What range of numbers do you think the "actual" volume of the water might fall in, based off of the measurement given by first cylinder? Based off of the second?

Solution:

When you read ​25mL​ on a scale marked every ​1mL, the water level must be closer to the ​25mL​ mark than to either the ​24mL​ or the ​26mL​ marks, but you do not know exactly where between them. The point where it would instead look closer to ​24mL​ is halfway between ​24​ and ​25, which is

​
224+25​=24.5
​

and the point where it would look closer to ​26mL​ is halfway between ​25​ and ​26, which is

​
225+26​=25.5
​

So any true volume between ​24.5mL​ and ​25.5mL​ would still be read as ​25mL. Therefore,

​
V∈[24.5,25.5]mL
​

On the ​0.25mL​-graduation cylinder, a reading of ​25.25mL​ means the water level is nearer the ​25.25​ mark than to ​25.00​ or ​25.50. The halfway points are

​
225.00+25.25​=25.125and225.25+25.50​=25.375
​

So any true volume between ​25.125mL​ and ​25.375mL​ would register as ​25.25mL, giving

​
V∈[25.125,25.375]mL
​

Approximations & Error (Lesson 3/3)

Error

1 / 12

Discussion

We saw in the rounding numbers section that the level of precision available when measuring values can impact the final answer of a calculation. Finding the volume of water in a graduated cylinder with markings every ​1​ ​mL,​ for example, could result in a different answer than finding the volume of the same amount of water in a different graduated cylinder that has markings every ​0.25​ ​mL.

Both of these cylinders have the same amount of water in them, but if we took the measurement using the first cylinder we'd get ​25​ ​mL,​ and if we took it using the second, we'd get ​25.25​ ​mL.

What range of numbers do you think the "actual" volume of the water might fall in, based off of the measurement given by first cylinder? Based off of the second?

Solution:

When you read ​25mL​ on a scale marked every ​1mL, the water level must be closer to the ​25mL​ mark than to either the ​24mL​ or the ​26mL​ marks, but you do not know exactly where between them. The point where it would instead look closer to ​24mL​ is halfway between ​24​ and ​25, which is

​
224+25​=24.5
​

and the point where it would look closer to ​26mL​ is halfway between ​25​ and ​26, which is

​
225+26​=25.5
​

So any true volume between ​24.5mL​ and ​25.5mL​ would still be read as ​25mL. Therefore,

​
V∈[24.5,25.5]mL
​

On the ​0.25mL​-graduation cylinder, a reading of ​25.25mL​ means the water level is nearer the ​25.25​ mark than to ​25.00​ or ​25.50. The halfway points are

​
225.00+25.25​=25.125and225.25+25.50​=25.375
​

So any true volume between ​25.125mL​ and ​25.375mL​ would register as ​25.25mL, giving

​
V∈[25.125,25.375]mL
​