QuestionCalculate the volume of a microchip with dimensions $w=4.456 \mathrm{~mm}$ , $h=0.0055 \mathrm{~mm}$ , $z=3.5$ . Round results in various formats and find percentage error.

Studdy Solution

STEP 1

Assumptions1. The width of the microchip is $w=4.456$ mm. The height of the microchip is $h=0.0055$ mm3. The depth of the microchip is $z=3.5$ mm4. The volume of the microchip can be calculated using the formula for the volume of a rectangular prism, which is $Volume = width \times height \times depth$

STEP 2

First, we need to calculate the exact volume of the microchip using the formula.
$Volume = w \times h \times z$

STEP 3

Now, plug in the given values for the width, height, and depth to calculate the volume.
$Volume =.456 \, mm \times0.0055 \, mm \times3.5 \, mm$

STEP 4

Calculate the exact volume of the microchip.
$Volume =4.456 \, mm \times0.005 \, mm \times3. \, mm =0.107694 \, mm^3$

STEP 5

Write the volume rounded to3 decimal places.
$Volume \approx0.108 \, mm^3$

STEP 6

Write the volume rounded to the nearest hundredths.
$Volume \approx0.11 \, mm^3$

STEP 7

Write the volume rounded to three significant figures.
$Volume \approx0.108 \, mm^3$

STEP 8

Write the answer in the form $a \times10^k$ , where $1<a<10, k \in Z$ .
$Volume \approx1.08 \times10^{-1} \, mm^3$

STEP 9

Calculate the percentage error between the exact volume and the volume rounded to the nearest hundredths. The formula for percentage error is $Percentage\, error = \left|\frac{Exact\, value - Approximate\, value}{Exact\, value}\right| \times100\%$

STEP 10

Plug in the values for the exact volume and the approximate volume to calculate the percentage error.
$Percentage\, error = \left|\frac{0.107694 \, mm^3 -0. \, mm^3}{0.107694 \, mm^3}\right| \times100\%$

STEP 11

Calculate the percentage error.
$Percentage\, error = \left|\frac{0.107694 \, mm^3 -0.11 \, mm^3}{0.107694 \, mm^3}\right| \times100\% =.14\%$

STEP 12

Write the percentage error rounded to2 significant figures.
$Percentage\, error \approx2.\%$

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QuestionCalculate the volume of a microchip with dimensions $w=4.456 \mathrm{~mm}$ , $h=0.0055 \mathrm{~mm}$ , $z=3.5$ . Round results in various formats and find percentage error.

Studdy Solution

STEP 1

STEP 2

First, we need to calculate the exact volume of the microchip using the formula.
$Volume = w \times h \times z$

STEP 3

Now, plug in the given values for the width, height, and depth to calculate the volume.
$Volume =.456 \, mm \times0.0055 \, mm \times3.5 \, mm$

STEP 4

Calculate the exact volume of the microchip.
$Volume =4.456 \, mm \times0.005 \, mm \times3. \, mm =0.107694 \, mm^3$

STEP 5

Write the volume rounded to3 decimal places.
$Volume \approx0.108 \, mm^3$

STEP 6

Write the volume rounded to the nearest hundredths.
$Volume \approx0.11 \, mm^3$

STEP 7

Write the volume rounded to three significant figures.
$Volume \approx0.108 \, mm^3$

STEP 8

Write the answer in the form $a \times10^k$ , where $1<a<10, k \in Z$ .
$Volume \approx1.08 \times10^{-1} \, mm^3$

STEP 9

Calculate the percentage error between the exact volume and the volume rounded to the nearest hundredths. The formula for percentage error is $Percentage\, error = \left|\frac{Exact\, value - Approximate\, value}{Exact\, value}\right| \times100\%$

STEP 10

Plug in the values for the exact volume and the approximate volume to calculate the percentage error.
$Percentage\, error = \left|\frac{0.107694 \, mm^3 -0. \, mm^3}{0.107694 \, mm^3}\right| \times100\%$

STEP 11

Calculate the percentage error.
$Percentage\, error = \left|\frac{0.107694 \, mm^3 -0.11 \, mm^3}{0.107694 \, mm^3}\right| \times100\% =.14\%$

STEP 12

Write the percentage error rounded to2 significant figures.
$Percentage\, error \approx2.\%$

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QuestionCalculate the volume of a microchip with dimensions w=4.456 mmw=4.456 \mathrm{~mm}w=4.456 mm, h=0.0055 mmh=0.0055 \mathrm{~mm}h=0.0055 mm, z=3.5z=3.5z=3.5. Round results in various formats and find percentage error.

Studdy Solution

STEP 1

STEP 2

First, we need to calculate the exact volume of the microchip using the formula.Volume=w×h×zVolume = w \times h \times zVolume=w×h×z

STEP 3

Now, plug in the given values for the width, height, and depth to calculate the volume.Volume=.456 mm×0.0055 mm×3.5 mmVolume =.456 \, mm \times0.0055 \, mm \times3.5 \, mmVolume=.456mm×0.0055mm×3.5mm

STEP 4

Calculate the exact volume of the microchip.Volume=4.456 mm×0.005 mm×3. mm=0.107694 mm3Volume =4.456 \, mm \times0.005 \, mm \times3. \, mm =0.107694 \, mm^3Volume=4.456mm×0.005mm×3.mm=0.107694mm3

STEP 5

Write the volume rounded to3 decimal places.Volume≈0.108 mm3Volume \approx0.108 \, mm^3Volume≈0.108mm3

STEP 6

Write the volume rounded to the nearest hundredths.Volume≈0.11 mm3Volume \approx0.11 \, mm^3Volume≈0.11mm3

STEP 7

Write the volume rounded to three significant figures.Volume≈0.108 mm3Volume \approx0.108 \, mm^3Volume≈0.108mm3

STEP 8

Write the answer in the form a×10ka \times10^ka×10k, where 1<a<10,k∈Z1<a<10, k \in Z1<a<10,k∈Z.Volume≈1.08×10−1 mm3Volume \approx1.08 \times10^{-1} \, mm^3Volume≈1.08×10−1mm3

STEP 9

STEP 10

STEP 11

Calculate the percentage error.Percentage error=∣0.107694 mm3−0.11 mm30.107694 mm3∣×100%=.14%Percentage\, error = \left|\frac{0.107694 \, mm^3 -0.11 \, mm^3}{0.107694 \, mm^3}\right| \times100\% =.14\%Percentageerror=∣∣​0.107694mm30.107694mm3−0.11mm3​∣∣​×100%=.14%

STEP 12

Write the percentage error rounded to2 significant figures.Percentage error≈2.%Percentage\, error \approx2.\%Percentageerror≈2.%

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QuestionCalculate the volume of a microchip with dimensions $w=4.456 \mathrm{~mm}$ , $h=0.0055 \mathrm{~mm}$ , $z=3.5$ . Round results in various formats and find percentage error.

First, we need to calculate the exact volume of the microchip using the formula.
$Volume = w \times h \times z$

Now, plug in the given values for the width, height, and depth to calculate the volume.
$Volume =.456 \, mm \times0.0055 \, mm \times3.5 \, mm$

Calculate the exact volume of the microchip.
$Volume =4.456 \, mm \times0.005 \, mm \times3. \, mm =0.107694 \, mm^3$

Write the volume rounded to3 decimal places.
$Volume \approx0.108 \, mm^3$

Write the volume rounded to the nearest hundredths.
$Volume \approx0.11 \, mm^3$

Write the volume rounded to three significant figures.
$Volume \approx0.108 \, mm^3$

Write the answer in the form $a \times10^k$ , where $1<a<10, k \in Z$ .
$Volume \approx1.08 \times10^{-1} \, mm^3$

Calculate the percentage error.
$Percentage\, error = \left|\frac{0.107694 \, mm^3 -0.11 \, mm^3}{0.107694 \, mm^3}\right| \times100\% =.14\%$

Write the percentage error rounded to2 significant figures.
$Percentage\, error \approx2.\%$