Option B
The first strain is [tex]2.182 \times 10^{-7}[/tex] mm larger than second strain
Solution:
Given that,
The length of one strain of the bacteria measures 0.000000242 mm
The length of the second strain measures 0.0000000238 mm
To find: Difference between the first strain and second strain
From given ,
Length of first strain = 0.000000242 mm
Length of second strain = 0.0000000238 mm
Let us convert them into scientific notation
Move the decimal point in your number until there is only one non-zero digit to the left of the decimal point. The resulting decimal number is a.
Count how many places you moved the decimal point. This number is b.
If you moved the decimal to the left b is positive.
If you moved the decimal to the right b is negative.
Write your scientific notation number as a x 10^b
Therefore,
[tex]0.000000242 = 2.42 \times 10^{-7}[/tex]
[ Here we moved the decimal point to right , we have moved 7 times. So exponent is -7 ]
[tex]0.0000000238 = 2.38 \times 10^{-8}[/tex]
[ Here we moved the decimal point to right , we have moved 8 times. So exponent is -8 ]
Now find the difference
[tex]Difference = length\ of\ first\ strain\ - length\ of\ second\ strain[/tex]
[tex]Difference = (2.42 \times 10^{-7}) - (2.38 \times 10^{-8})\\\\\text{Make the exponents same }\\\\Difference = (2.42 \times 10^{-7}) - (0.238 \times 10^{-7})\\\\\text{Take the common term out }\\\\Difference = 10^{-7}(2.42 - 0.238)\\\\Difference = 10^{-7} \times 2.182\\\\Difference = 2.182 \times 10^{-7}[/tex]
Thus first strain is [tex]2.182 \times 10^{-7}[/tex] mm larger than second
