The size of a cell is typically found by capturing an image under a microscope then using software to measure its diameter. Two cells are measured using this method:
Cell C: 4, point, 1, 6, times, 10, to the power minus 24.16×10
−2
centimeters
Cell D: 9, point, 5, times, 10, to the power minus 49.5×10
−4
centimeters
How much larger is the diameter of cell C than the diameter of cell D? Express your answer using scientific notation.
To determine how much larger the diameter of cell C is compared to cell D, we need to calculate the ratio of their diameters.
Ratio = Diameter of Cell C / Diameter of Cell D
Using scientific notation, the diameters are as follows:
Diameter of Cell C = 4.16 × 10^(-2) cm
Diameter of Cell D = 9.5 × 10^(-4) cm
Let's divide the diameter of Cell C by the diameter of Cell D:
Ratio = (4.16 × 10^-2) / (9.5 × 10^-4)
To divide numbers in scientific notation, we subtract the exponents and divide the coefficients:
Ratio = (4.16 / 9.5) × (10^-2 / 10^-4)
Simplifying the exponents:
Ratio = (4.16 / 9.5) × 10^(-2 - (-4))
= (4.16 / 9.5) × 10^(-2 + 4)
= (4.16 / 9.5) × 10^2
Using a calculator, we can find the numeric value of the ratio:
Ratio ≈ 0.4368421053 × 100
≈ 43.68421053
Expressing the ratio in scientific notation:
Ratio ≈ 4.368421053 × 10^1
Therefore, the diameter of cell C is approximately 43.68 times larger than the diameter of cell D.
To determine the difference in size between cell C and cell D, we need to subtract the diameter of cell D from the diameter of cell C.
The diameter of cell C is given as 4.1 × 10^(-24.16) centimeters.
The diameter of cell D is given as 9.5 × 10^(-49.5) centimeters.
To subtract these numbers, we need to have the exponents of 10 in the scientific notation to be the same. In this case, we can convert the exponents of both numbers to the largest exponent, which is -24.16.
To convert the diameter of cell D to -24.16 × 10^(-2) centimeters, we need to multiply the given diameter by 10^(24.16 - (-2)) = 10^(26.16) to make the exponents match.
So, the diameter of cell D is 9.5 × 10^(-49.5) × 10^(26.16) = 9.5 × 10^(-49.5 + 26.16) = 9.5 × 10^(-23.34) centimeters.
Now that we have both diameters in the same scientific notation format, we can subtract them:
(4.1 × 10^(-24.16)) - (9.5 × 10^(-23.34))
To subtract these two numbers, we need to have the same exponent. Therefore, we need to convert one of the numbers to match the exponent of the other. In this case, we can convert both numbers to 10^(-24.16) as the matching exponent.
(4.1 × 10^(-24.16)) - (9.5 × 10^(-23.34)) = (4.1 × 10^(-24.16)) - (9.5 × 10^(-24.16))
Now, we can subtract the two numbers:
4.1 - 9.5 = -5.4
Therefore, the diameter of cell C is 5.4 times larger than the diameter of cell D.
Expressing this difference in scientific notation format, the diameter of cell C is 5.4 × 10^0 times larger than the diameter of cell D.
To find the difference in diameter between cell C and cell D, we need to subtract the diameter of cell D from the diameter of cell C.
The diameter of cell C is 4.16 × 10^(-2) cm and the diameter of cell D is 9.5 × 10^(-4) cm.
To subtract the two numbers, we need to convert them to the same power of 10. In this case, let's convert them to the same power of 10 as the larger number, which is 10^(-2).
The diameter of cell D in scientific notation with a power of 10^(-2) is 0.95 × 10^(-2) cm.
Now we can subtract the two numbers:
4.16 × 10^(-2) cm - 0.95 × 10^(-2) cm = 3.21 × 10^(-2) cm.
Therefore, the diameter of cell C is 3.21 × 10^(-2) cm larger than the diameter of cell D.