Question

17 points sorry that all I have right now

Scientists are examining two different strains of a particular bacteria. The length of one strain of the bacteria measures 0.000000242 mm, while the length of the second strain measures 0.0000000238 mm. How much larger is the first strain than the second?

A.

2.658 × 10-7 mm

B.

2.182 × 10-7 mm

C.

2.182 × 10-8 mm

D.

2.658 × 10-15 mm

Answer 1

Option B

The first strain is
`2.182 * 10^(-7)` 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,

`0.000000242 = 2.42 * 10^(-7)`

[ Here we moved the decimal point to right , we have moved 7 times. So exponent is -7 ]

`0.0000000238 = 2.38 * 10^(-8)`

[ Here we moved the decimal point to right , we have moved 8 times. So exponent is -8 ]

Now find the difference

`Difference = length\ of\ first\ strain\ - length\ of\ second\ strain`

`Difference = (2.42 * 10^(-7)) - (2.38 * 10^(-8))\\\\\text{Make the exponents same }\\\\Difference = (2.42 * 10^(-7)) - (0.238 * 10^(-7))\\\\\text{Take the common term out }\\\\Difference = 10^(-7)(2.42 - 0.238)\\\\Difference = 10^(-7) * 2.182\\\\Difference = 2.182 * 10^(-7)`

Thus first strain is
`2.182 * 10^(-7)` mm larger than second