Scientists are examining two different strains of a particular bacteria. The length of one strain of the bacteria measures 0.000000144 mm, while the length of the second strain measures 0.0000000818 mm. How much larger is the first strain than the second?

3 answers

To find out how much larger the first strain of the bacteria is compared to the second strain, we can subtract the length of the second strain from the length of the first strain.

The lengths of the bacteria strains are as follows:

  • First strain: \( 0.000000144 , \text{mm} \)
  • Second strain: \( 0.0000000818 , \text{mm} \)

Now, let's perform the subtraction:

\[ 0.000000144 , \text{mm} - 0.0000000818 , \text{mm} \]

To make the subtraction clearer, it can help to align the numbers:

\[ \begin{array}{r} 0.000000144 \

  • 0.0000000818 \ \hline \end{array} \]

We can also write \( 0.0000000818 \) as \( 0.00000008180 \) for easier subtraction:

\[ \begin{array}{r} 0.00000014400 \

  • 0.00000008180 \ \hline \end{array} \]

Now, let’s perform the subtraction digit by digit from the right:

  • From the last two decimal places: \( 0 - 0 = 0 \)
  • Next places: \( 4 - 8 \): we can't do this directly, so we take 1 from the previous digit (making it 3) and turn the current digit into \( 14 \):
    • \( 14 - 8 = 6 \)
  • Then we have: \( 3 - 1 = 2 \)
  • Finally, the leading digits: \( 0 - 0 = 0 \)

Putting this together, we get:

\[ 0.00000014400 - 0.00000008180 = 0.0000000622 \]

So, the difference between the two strains is:

\[ 0.0000000622 , \text{mm} \]

Thus, the first strain is longer by 0.0000000622 mm than the second strain.

answer in scientific notation

To express \(0.0000000622 , \text{mm}\) in scientific notation, we can rewrite it as follows:

  1. Move the decimal point to the right until there is only one non-zero digit to its left. In this case, we move the decimal point 8 places to the right, which gives us \(6.22\).
  2. Since we moved the decimal point 8 places to the right, we multiply by \(10^{-8}\).

Thus, \(0.0000000622\) in scientific notation is:

\[ 6.22 \times 10^{-8} , \text{mm} \]

So the first strain is longer by \(6.22 \times 10^{-8} , \text{mm}\) compared to the second strain.