Question

4.1: scientific notation (due tuesday, september 9)
score: 19/24 answered: 10/11
question 9
a) a human red blood cell is 0.000 007 meters in diameter. write that in scientific notation.
0.000 007 meters = \boxed{} meters
b) a needle used for drawing blood has an opening 0.531 millimeters wide. 1 millimeter = $10^{-3}$ meters, so the needle is $0.531 \times 10^{-3}$ meters wide. write this number in scientific notation.
0.531 millimeters = \boxed{} meters

Explanation:

Part (a)

Step1: Identify the coefficient and exponent

To convert \(0.000007\) to scientific notation, we move the decimal point to the right until we have a number between \(1\) and \(10\). We move it 6 places to the right, so the exponent of \(10\) will be \(-6\) (since we moved it to the right in a small number). The coefficient is \(7\).
\(0.000007 = 7\times10^{-6}\)

Step2: Write the final scientific notation

So, \(0.000007\) meters in scientific notation is \(7\times10^{-6}\) meters.

Part (b)

Step1: Simplify the given expression

We have \(0.531\times10^{-3}\). In scientific notation, the coefficient should be between \(1\) and \(10\). We can rewrite \(0.531\) as \(5.31\times10^{-1}\). Then we multiply the powers of \(10\): \(10^{-1}\times10^{-3}=10^{-1 + (-3)} = 10^{-4}\)
\(0.531\times10^{-3}=5.31\times10^{-1}\times10^{-3}=5.31\times10^{-4}\)

Step2: Write the final scientific notation

So, \(0.531\) millimeters is \(5.31\times10^{-4}\) meters.

Answer:

a) \(7\times10^{-6}\)
b) \(5.31\times10^{-4}\)