Math Snap

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

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