A company is designing a rectangular computer chip that is 8.14 × 10−7 meters long and 3.6 × 10−9 meters wide.
Part A: Determine the area of the computer chip. Show every step of your work.
Part B: Write the area in scientific notation with the correct number of significant digits, and label with the appropriate units. (3 points)
Part C: Determine the perimeter of the computer chip. Show every step of your work.
Part D: Write the perimeter in scientific notation with the correct number of significant digits, and label with the appropriate units.
Part A:
To determine the area of the computer chip, we can multiply the length by the width.
Area = length × width
Area = (8.14 × 10^(-7)) m × (3.6 × 10^(-9)) m
When multiplying numbers written in scientific notation, we can multiply the coefficients (8.14 × 3.6) and add the exponents of 10 (-7 + -9).
Area = 8.14 × 3.6 × 10^(-7 + -9)
Area = 29.304 × 10^(-16)
So, the area of the computer chip is 29.304 × 10^(-16) square meters.
Part B:
To write the area in scientific notation with the correct number of significant digits, we need to determine how many significant digits are in the coefficients (29.304). Both numbers in the multiplication have 4 significant digits, so we have 4 significant digits in the product.
Therefore, the area of the computer chip in scientific notation with the correct number of significant digits is 2.9304 × 10^(-15) square meters.
Part C:
To determine the perimeter of the computer chip, we need to add up the lengths of all four sides.
Perimeter = 2 × (length + width)
Perimeter = 2 × ((8.14 × 10^(-7)) m + (3.6 × 10^(-9)) m)
Perimeter = 2 × (8.14 × 10^(-7)) m + 2 × (3.6 × 10^(-9)) m
Perimeter = 2 × 8.14 × 10^(-7) m + 2 × 3.6 × 10^(-9) m
Perimeter = 16.28 × 10^(-7) m + 7.2 × 10^(-9) m
Part D:
To write the perimeter in scientific notation with the correct number of significant digits, we need to determine how many significant digits are in the coefficients (16.28 and 7.2). Both numbers have 3 significant digits, so we have 3 significant digits in the sum.
Therefore, the perimeter of the computer chip in scientific notation with the correct number of significant digits is 2.34 × 10^(-8) meters.
Part A: To determine the area of the computer chip, we need to multiply its length by its width.
Given:
Length = 8.14 × 10^(-7) meters
Width = 3.6 × 10^(-9) meters
Area = Length x Width
Calculating the area:
Area = (8.14 × 10^(-7)) x (3.6 × 10^(-9))
Area = (8.14 x 3.6) × (10^(-7) x 10^(-9))
Area = 29.304 × 10^(-7-9)
Simplifying the exponential notation:
Area = 29.304 × 10^(-16)
Part B: To write the area in scientific notation with the correct number of significant digits and label with the appropriate units, we can express it as follows:
Area = 2.93 × 10^(-15) m^2
Part C: To determine the perimeter of the computer chip, we need to add up all four sides of the rectangle.
Given:
Length = 8.14 × 10^(-7) meters
Width = 3.6 × 10^(-9) meters
Perimeter = 2(Length + Width)
Calculating the perimeter:
Perimeter = 2((8.14 × 10^(-7)) + (3.6 × 10^(-9)))
Perimeter = 2(8.14 × 10^(-7) + 3.6 × 10^(-9))
Perimeter = 2(8.14 × 10^(-7)) + 2(3.6 × 10^(-9))
Perimeter = (2 × 8.14) × (10^(-7)) + (2 × 3.6) × (10^(-9))
Perimeter = 16.28 × 10^(-7) + 7.2 × 10^(-9)
Simplifying the exponential notation:
Perimeter = 16.28 × 10^(-7) + 0.72 × 10^(-7)
Combining like terms:
Perimeter = 17 × 10^(-7) meters
Part D: To write the perimeter in scientific notation with the correct number of significant digits and label with the appropriate units, we can express it as follows:
Perimeter = 1.7 × 10^(-6) m
Part A:
To determine the area of the computer chip, we can use the formula for the area of a rectangle, which is given by the product of its length and width.
The length of the computer chip is 8.14 × 10^(-7) meters, and the width is 3.6 × 10^(-9) meters.
Multiplying these two values together, we get:
Area = (8.14 × 10^(-7) m) * (3.6 × 10^(-9) m)
= 29.304 × 10^(-16) m^2
Part B:
To write the area in scientific notation with the correct number of significant digits, we need to consider the significant digits in the given values (length and width).
The length of the chip, 8.14 × 10^(-7), has three significant digits, and the width, 3.6 × 10^(-9), has two significant digits.
Since multiplication involves multiplying significant digits, we need to take the smaller number of significant digits, which is two, for our final answer.
Therefore, the area can be written as:
Area = 29 × 10^(-16) m^2
Note that we rounded down to two significant digits because of the width, and we preserved the units (m^2).
Part C:
To determine the perimeter of the computer chip, we can use the formula for the perimeter of a rectangle, which is given by twice the sum of its length and width.
The length of the computer chip is 8.14 × 10^(-7) meters, and the width is 3.6 × 10^(-9) meters.
The perimeter can be calculated as:
Perimeter = 2 * (8.14 × 10^(-7) m + 3.6 × 10^(-9) m)
= 2 * (8.14 × 10^(-7) m + 0.0036 × 10^(-7) m)
= 2 * (8.1436 × 10^(-7) m)
= 16.2872 × 10^(-7) m
Part D:
To write the perimeter in scientific notation with the correct number of significant digits, we need to consider the significant digits in the given values (length and width).
The length of the chip, 8.14 × 10^(-7), has three significant digits, and the width, 3.6 × 10^(-9), has two significant digits.
Since addition involves adding the values of the same order of magnitude, we can keep the three significant digits for our final answer.
Therefore, the perimeter can be written as:
Perimeter = 16.3 × 10^(-7) m
Note that we rounded up to three significant digits, and we preserved the units (m).