The length of a bacterial cell is about 5 x 10−6 m, and the length of an amoeba cell is about 3.5 x 10−4 m. How many times smaller is the bacterial cell than the amoeba cell? Write the final answer in scientific notation with the correct number of significant digits.
a) 1.4 x 101
b) 7 x 101
c) 143 x 101
d) 7 x 103
To find how many times smaller the bacterial cell is than the amoeba cell, we can divide the length of the amoeba cell by the length of the bacterial cell:
(3.5 x 10^-4 m) / (5 x 10^-6 m)
To divide these numbers, we can subtract the exponents of the scientific notation and divide the coefficients:
3.5 / 5 = 0.7
Now let's calculate the difference in exponents:
(-4) - (-6) = -4 + 6 = 2
The final answer can be written as 0.7 x 10^2, or 0.7 x 100. Since the coefficient is less than 10, it can be also written as 7 x 10^1.
Therefore, the bacterial cell is 7 times smaller than the amoeba cell, and the answer is d) 7 x 10^1.
To determine the number of times smaller the bacterial cell is than the amoeba cell, we need to calculate the ratio of their lengths.
The ratio can be found by dividing the length of the bacterial cell by the length of the amoeba cell:
Ratio = Length of bacterial cell / Length of amoeba cell
Ratio = (5 x 10^-6 m) / (3.5 x 10^-4 m)
Next, divide the values in the numerator and denominator:
Ratio = (5 / 3.5) x (10^-6 / 10^-4)
Simplify the fraction:
Ratio = 1.428571428571429 x 10^-2
Finally, write the ratio in scientific notation with the correct number of significant digits. Since the length of the bacterial cell is given to two significant digits (5), the final answer should also have two significant digits:
Ratio = 1.4 x 10^-2
Thus, the bacterial cell is 1.4 x 10^1 times smaller than the amoeba cell.
The correct answer is a) 1.4 x 10^1.
To find out how many times smaller the bacterial cell is compared to the amoeba cell, we need to divide the length of the amoeba cell by the length of the bacterial cell.
The length of the bacterial cell is 5 x 10^-6 m.
The length of the amoeba cell is 3.5 x 10^-4 m.
To divide these lengths, we need to subtract their exponents. In this case, we have to subtract -6 from -4.
(-4) - (-6) = -4 + 6 = 2
Now we divide the significant figures (not the exponents):
3.5 ÷ 5 = 0.7
Combining the exponent and significant figures, we get:
0.7 x 10^2
However, in scientific notation, the significant figures should be between 1 and 10. So we need to shift the decimal point one place to the right, which results in:
7 x 10^1
Therefore, the final answer is:
b) 7 x 10^1