Question

the human eye contains approximately $9.1 \times 10^7$ rod cells and $4.5 \times 10^6$ cone cells. sam subtracts $9.1 - 4.5$ and says there are about 46,000,000 more rod cells than cone cells. use the drop-down menus to explain why sam is incorrect. click the arrows to choose an answer from each menu. before subtracting the decimal numbers, sam should have written $4.5 \times 10^6$ as choose.... there are choose... more rod cells than cone cells.

Explanation:

Step1: Convert to same exponent

To subtract numbers in scientific notation, exponents must match. Convert \(4.5 \times 10^6\) to \(0.45 \times 10^7\) (since \(10^6 = 0.1 \times 10^7\), so \(4.5 \times 10^6 = 4.5 \times 0.1 \times 10^7 = 0.45 \times 10^7\)).

Step2: Subtract the decimals

Now subtract the coefficients: \(9.1 - 0.45 = 8.65\).

Step3: Write in scientific notation

The result is \(8.65 \times 10^7\), which is \(86500000\) in standard form.

Answer:

Before subtracting the decimal numbers, Sam should have written \(4.5 \times 10^6\) as \(0.45 \times 10^7\). There are \(8.65 \times 10^7\) (or \(86500000\)) more rod cells than cone cells.