Question

question
the size of a cell is typically found by capturing an image under a microscope then using software to measure its diameter. two cells are measured using this method:

cell a: $5.47 \times 10^{-3}$ centimeters
cell b: $8.6 \times 10^{-4}$ centimeters

how much larger is the diameter of cell a than the diameter of cell b? express your answer using either standard notation or scientific notation.

answer attempt 1 out of 2

standard notation

Explanation:

Step1: Make exponents same

To subtract the two numbers in scientific notation, we first make the exponents of 10 the same. We know that \(5.47\times 10^{-3}=54.7\times 10^{-4}\) (since moving the decimal point one place to the right in the coefficient increases the exponent of 10 by 1, so \(- 3+ 1=-4\)).

Step2: Subtract the coefficients

Now we subtract the coefficient of Cell B from the coefficient of the rewritten Cell A. So we have \((54.7 - 8.6)\times10^{-4}\). Calculating \(54.7-8.6 = 46.1\), so we get \(46.1\times 10^{-4}\).

Step3: Convert to standard or scientific notation

We can convert \(46.1\times 10^{-4}\) to standard notation by moving the decimal point 4 places to the left (because of the negative exponent). So \(46.1\times 10^{-4}=0.00461\). Or we can write it in scientific notation as \(4.61\times 10^{-3}\) (by moving the decimal point one place to the left in the coefficient and increasing the exponent of 10 by 1).

Answer:

\(0.00461\) (or \(4.61\times 10^{-3}\))