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.

1 answer

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.