Question

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 × 10⁻³ meters wide. write this number in scientific notation.
0.531 millimeters = \boxed{} meters
c) divide the width of the needle by the diameter of a red blood cell. in other words, divide your answer from (b) by your answer from (a). give your answer in standard notation. round to the nearest whole number.
\boxed{}
d) which is the best interpretation of the number you found in part (c)?
○ the width of the needle is ___ meters longer than the diameter of a red blood cell.
○ the width of the needle is ___ times the diameter of a red blood cell.
○ the diameter of a red blood cell is ___ meters longer than the width of the needle.
○ the diameter of a red blood cell is ___ times the width of the needle.

Explanation:

Part (b)

Step1: Recall scientific notation rules

Scientific notation is in the form \( a \times 10^{n} \), where \( 1 \leq |a| < 10 \) and \( n \) is an integer. We have \( 0.531\times10^{-3} \). To get \( a \) between 1 and 10, we move the decimal point one place to the right, so we decrease the exponent by 1.

Step2: Rewrite the number

\( 0.531\times10^{-3}=5.31\times10^{-4} \) (since \( 0.531 = 5.31\times10^{-1} \), so \( 5.31\times10^{-1}\times10^{-3}=5.31\times10^{-4} \))

Step1: Identify the two numbers

Needle width (from b): \( 5.31\times10^{-4} \) meters. Red blood cell diameter (from a): \( 7\times10^{-6} \) meters.

Step2: Perform the division

\( \frac{5.31\times10^{-4}}{7\times10^{-6}}=\frac{5.31}{7}\times10^{-4 - (-6)} \)

Step3: Calculate the coefficient and exponent

\( \frac{5.31}{7}\approx0.7586 \), \( 10^{-4+6}=10^{2} \), so \( 0.7586\times10^{2}=75.86\approx76 \) (rounded to nearest whole number)

We divided the needle's width by the red blood cell's diameter, so the result represents how many times the needle's width is compared to the cell's diameter. The first option is about length difference (we did division, not subtraction), third and fourth are incorrect as we divided needle width by cell diameter (so needle is larger in this case).

Answer:

\( 5.31\times 10^{-4} \)

Part (c)

(Assuming part (a) gave the diameter of a red blood cell as \( 7\times10^{-6} \) meters, a common value. If not, adjust accordingly. Let's proceed with this assumption for demonstration.)