Beth is given the following question - OCR - GCSE Maths - Question 22 - 2017 - Paper 1

To solve the expression $4.1 \times 10^5 \times 3 \times 10^2$, first, we multiply the coefficients and then add the exponents of the powers of 10.

1. Multiply Coefficients:

   $4.1 \times 3 = 12.3$

2. Add Exponents:

   $10^5 \times 10^2 = 10^{5+2} = 10^7$

So, the correct calculation gives:

$12.3 \times 10^7$

Beth's answer appears to be accurate at first, but the common mistake she made might be related to the placement of the decimal point when converting to standard form. If her final result is presented without normalizing (keeping the coefficient between 1 and 10), it would be inaccurate. Thus her answer should be presented as:

$1.23 \times 10^8$.