The approximate mass of the earth is $5.976 \times 10^{24}$ kg. How many times is the earth heavier than an average male adult who weighs 75 kg? Give your answer in standard form correct to 3 significant figures. Answer: ... The sum of 3 consecutive even numbers is estimated to be 300 when rounded off to 1 significant figure. Find the largest possible set of the 3 numbers. Answer: ... , ... , ...

1. Form the ratio and calculate how many times heavier the earth is.

$\frac{5.976\times 10^{24}}{75}=7.968\times 10^{22}$

2. Round the answer to 3 significant figures in standard form.

$7.968\times 10^{22}=7.97\times 10^{22}\quad \text{to 3 s.f.}$

1. Find the possible range of sums that round to 300 to 1 significant figure.

To 1 significant figure, numbers from $250$ up to $349$ round to $300$.

So the sum must be a whole number with
$250 \leq \text{sum} \leq 349.$

2. Choose the largest possible sum that is compatible with 3 consecutive even numbers.

The sum of 3 consecutive even numbers is even, since
$(n-2)+n+(n+2)=3n,$
where $n$ is even, so $3n$ is even.

The largest even sum not exceeding $349$ is $348$.

3. Find the 3 consecutive even numbers with this largest possible sum.

Let the 3 consecutive even numbers be $x-2$, $x$, $x+2$.

$(x-2)+x+(x+2)=348$
$3x=348$
$x=116$

So the numbers are
$114,\ 116,\ 118.$