SL 1.1—Using standard form

We need $\frac{6.39\times 10^{23}}{7.34\times 10^{22}}$. Divide the $a$ values and subtract the exponents.

$\frac{6.39}{7.34}\approx 0.8706\approx 0.871$

$10^{23-22}=10^1$ So the intermediate result is $0.871\times 10^1$.

$0.871\times 10^1=8.71\times 10^0$ since $0.871=8.71\times 10^{-1}$, giving $8.71\times 10^{-1}\times 10^1=8.71\times 10^0$.

Since $1\le 8.71<10$ and the exponent is $0$ (an integer), the answer $8.71\times 10^0$ is in valid standard form.

We need the ratio of Mars's mass to the Moon's mass in standard form. Mars is roughly 8–9 times heavier, so the answer should be close to $8.7$.

$8.71\times 10^1=87.1$, which would mean Mars is 87 times heavier than the Moon. That is too large given the exponents differ by only 1.

$8.71\times 10^{-1}=0.871$, implying Mars is lighter than the Moon. Since $10^{23}>10^{22}$, Mars must be heavier, so this is impossible.

$8.71\times 10^2=871$, meaning Mars is 871 times heavier. The masses differ by only one power of 10, so this is far too large.

$8.71\times 10^0=8.71$ is consistent with a ratio where the exponents differ by 1 and the coefficient ratio is about $0.87$, giving $8.71$ after adjustment. This is the correct answer.

Month 1: $3.6\times 10^6$ kWh. Each month increases by $2.4\times 10^5$ kWh. Month 3 = Month 1 + 2 increases.

$2\times 2.4\times 10^5=4.8\times 10^5$

Express $3.6\times 10^6$ as $36.0\times 10^5$ so both terms share the same power of 10.

$36.0\times 10^5+4.8\times 10^5=40.8\times 10^5$

$40.8\times 10^5=4.08\times 10^6$ since $40.8=4.08\times 10^1$. The answer is $4.08\times 10^6$ kWh.

We need month 3 production, which equals month 1 production plus two increases of $2.4\times 10^5$ each.

This equals the first month production with no increase applied. It ignores the two monthly increases entirely.

$3.84\times 10^6-3.6\times 10^6=0.24\times 10^6=2.4\times 10^5$. This is only one increase, giving the second month, not the third.

$4.32\times 10^6-3.6\times 10^6=0.72\times 10^6=7.2\times 10^5=3\times 2.4\times 10^5$. This applies three increases, giving month 4 production.

$4.08\times 10^6-3.6\times 10^6=4.8\times 10^5=2\times 2.4\times 10^5$, confirming two increases have been applied. This is the third month.