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Pearson Algebra 1 Common Core, 2011

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Pearson Algebra 1 Common Core, 2011 View details

10. Change Expressed as a Percent

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Exercise 24 Page 149

First, find the minimum and maximum possible dimensions. Then, find the minimum and maximum possible areas.

About 4.7 %

Practice makes perfect

We know that the side lengths of the rectangle shown below have been measured to the nearest half of a meter. We need to find the greatest possible percent error when calculating its area.

Let's start by calculating the measured area.

A = width * length

width= 7.5 m, lenght= 18.5 m

A = 7.5 m * 18.5 m

Multiply

A = 138.75 m^2

Hence, the measured area is 138.75 square meters.

Finding Minimum and Maximum Possible Areas

When rounding measurements, the maximum error is equal to half of the lowest measuring unit. Thus, when measuring to the nearest half of a meter the maximum error is 0.25 meters. With this in mind, let's calculate the minimum possible dimensions of the rectangle. Minimum Width:& 7.5-0.25 = 7.25 Minimum Length:& 18.5 -0.25 = 18.25 We can now calculate the minimum possible area by substituting w_(min)= 7.25 m and l_(min)= 18.25 m.

A_(min) = w_(min) * l_(min)

w_(min)= 7.25, l_(min)= 18.25

A = 7.25 * 18.25

Multiply

A = 132.3125

On the other hand, the maximum possible dimensions are as follows. Maximum Width:& 7.5 +0.25 = 7.75 Maximum Length:& 18.5 +0.25 = 18.75 We can, similarly, calculate the maximum possible area.

A_(max) = w_(max) * l_(max)

w_(max)= 7.75, l_(max)= 18.75

A = 7.75 * 18.75

Multiply

A = 145.3125 m^2

Let's show what we have found so far in a table.

	Minimum	Maximum
Width (m)	7.5-0.25= 7.25	7.5+0.25= 7.75
Length (m)	18.5-0.25= 18.25	18.5+0.25= 18.75
Area (m^2 )	7.25 * 18.25 = 132.3125	7.75 * 18.75 = 145.3125

Finding the Greatest Possible Percent Error

We will now find the difference between the minimum possible area and the measured area.

| \ A_\text{min} - A \ |

A_\text{min}={\color{#0000FF}{132.3125}}, A= 138.75

| 132.3125 - 138.75 |

Subtract term

| - 6.4375 |

|-6.4375 |=6.4375

6.4375

Similarly, we can calculate the difference between the maximum possible area and the measured area.

| \ A_\text{max} - A \ |

A_\text{max}={\color{#0000FF}{145.3125}}, A= 138.75

| 145.3125 - 138.75 |

Subtract term

| 6.5625 |

|6.5625|=6.5625

6.5625

We can see that the greater difference happens for the maximum possible area. 6.5625 m^2 > 6.4375 m^2 We will use that difference when calculating the greatest percent error.

Percent Error = ( Greater difference in area/Measured area ) * 100

greater difference in area= 6.5625, measured area= 138.75

Percent Error = (6.5625/138.75) * 100

CancelCommonFac

Cancel out common factors

Percent Error = (6.5625/138.75) * 100

Use a calculator

Percent Error = (0.04729 ... ) * 100

Round to 3 decimal place(s)

Percent Error ≈ (0.047) * 100

Multiply

Percent Error ≈ 4.7 %

Therefore, the greatest possible percent error when calculating the area is about 4.7 %.

Subchapter links

Lesson Check p.148

Practice and Problem-Solving Exercises p.148-150

Standardized Test Prep p.150

Mixed Review p.150