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 G: 9, point, 2, 3, times, 10, to the power minus 39.23×10
−3
centimeters
Cell H: 4, point, 2, times, 10, to the power minus 44.2×10
−4
centimeters
How much larger is the diameter of cell G than the diameter of cell H? Express your answer using scientific notation.
To find the difference in diameter between cell G and cell H, we first need to convert both measurements to scientific notation.
Cell G: 9.2 x 10^(-39.23) cm
Cell H: 4.2 x 10^(-44.2) cm
To compare the sizes in scientific notation, we need to divide the diameter of cell G by the diameter of cell H:
(9.2 x 10^(-39.23)) / (4.2 x 10^(-44.2))
To divide numbers in scientific notation, we subtract the exponents:
9.2 / 4.2 x 10^((-39.23) - (-44.2))
Simplifying the exponents:
9.2 / 4.2 x 10^(4.97)
Now, since 10^4.97 is larger than 10^4, we can express the division in scientific notation:
(9.2 / 4.2) x 10^0.97
Dividing the decimal part:
2.19 x 10^0.97
So, the diameter of cell G is approximately 2.19 x 10^0.97 times larger than the diameter of cell H.
To determine the difference in diameter between the two cells, we need to calculate the ratio of their sizes. Let's start by converting the given measurements to standard exponential notation:
Cell G: 9.2 × 10^(-39.23) cm
Cell H: 4.2 × 10^(-44.2) cm
To find the ratio, we divide the diameter of Cell G by the diameter of Cell H:
Ratio = (9.2 × 10^(-39.23)) / (4.2 × 10^(-44.2))
To simplify this calculation, we can divide the coefficients (9.2 by 4.2) and subtract the exponents (-39.23 by -44.2):
Ratio = (9.2 / 4.2) × 10^(-39.23 - (-44.2))
= 2.19 × 10^(4.97)
The result gives us the ratio of the diameters of Cell G to Cell H as 2.19 × 10^4.97.
To find out how much larger the diameter of cell G is than the diameter of cell H, we need to subtract the diameter of cell H from the diameter of cell G.
First, let's convert the given measurements into scientific notation.
Cell G: 9.2 × 10^(-3) centimeters
Cell H: 4.2 × 10^(-4) centimeters
To subtract these numbers, we need to ensure that the exponents are the same. In this case, we can rewrite the diameter of cell G as:
9.2 × 10^(-3) = 9.2 × 10^(-4) × 10
Now, we can subtract the two numbers:
9.2 × 10^(-4) × 10 - 4.2 × 10^(-4) = 5 × 10^(-4)
Therefore, the diameter of cell G is 5 × 10^(-4) centimeters larger than the diameter of cell H.