Question

marcus was bored in science class and pulled out 3 strands of hair to compare under the microscope. he measured the strands to be $3.15\times10^{-3}$ inches, $3.94\times10^{-3}$ inches, and $3.02\times10^{-3}$ inches thick. what is the combined thickness of all 3 strands of hair? ______ inches

Explanation:

Step1: Identify the values to add

We have three thicknesses: \(3.15\times10^{-3}\) inches, \(3.94\times10^{-3}\) inches, and \(3.02\times10^{-3}\) inches. Since they all have the same exponent of \(10^{-3}\), we can add the coefficients first.

Step2: Add the coefficients

Add \(3.15 + 3.94 + 3.02\).
\(3.15+3.94 = 7.09\), then \(7.09 + 3.02 = 10.11\).

Step3: Combine with the power of 10

Now, we multiply the sum of the coefficients by \(10^{-3}\). So we have \(10.11\times10^{-3}\) inches. But we can rewrite this in proper scientific notation or just as a decimal. \(10.11\times10^{-3}=0.01011\) inches.

Answer:

\(0.01011\) (or \(1.011\times10^{-2}\) in scientific notation, but the decimal form is also correct here)