Comparing/calculating very large and small quantities

1. Order from smallest to largest: $3.2\times {10}^5$, $7.4\times {10}^4$, $2.9\times {10}^5$.

   2 marks
2. Calculate $\left(4\times {10}^3\right)\left(2\times {10}^5\right)$.

   2 marks
3. Calculate $\frac{9\times {10}^7}{3\times {10}^2}$.

   2 marks
4. Calculate $2.4\times {10}^6+5\times {10}^5$.

   2 marks
5. Calculate $\left(8\times {10}^{-3}\right)\left(5\times {10}^{-4}\right)$.

   2 marks
6. A file of $6\times {10}^8$ bytes is sent at $2\times {10}^6$ bytes per second. Find the time, assuming a constant rate.

   3 marks

Equivalent correct methods earn the corresponding marks. Include units where asked.

1. Order from smallest to largest: $3.2\times {10}^5$, $7.4\times {10}^4$, $2.9\times {10}^5$.

   2 marks

   The ${10}^4$ quantity is smaller than both ${10}^5$ quantities.

   For matching powers compare 2.9 with 3.2.

   $7.4\times {10}^4,2.9\times {10}^5,3.2\times {10}^5$
2. Calculate $\left(4\times {10}^3\right)\left(2\times {10}^5\right)$.

   2 marks

   $4\times 2=8$ and $3+5=8$.

   $8\times {10}^8$
3. Calculate $\frac{9\times {10}^7}{3\times {10}^2}$.

   2 marks

   $9÷3=3$ and $7-2=5$.

   $3\times {10}^5$
4. Calculate $2.4\times {10}^6+5\times {10}^5$.

   2 marks

   $5\times {10}^5=0.5\times {10}^6$.

   $\left(2.4+0.5\right)\times {10}^6=2.9\times {10}^6$.

   $2.9\times {10}^6$
5. Calculate $\left(8\times {10}^{-3}\right)\left(5\times {10}^{-4}\right)$.

   2 marks

   $8\times 5=40$ and $-3+\left(-4\right)=-7$.

   $40\times {10}^{-7}=4\times {10}^{-6}$.

   $4\times {10}^{-6}$
6. A file of $6\times {10}^8$ bytes is sent at $2\times {10}^6$ bytes per second. Find the time, assuming a constant rate.

   3 marks

   $t=\frac{6\times {10}^8}{2\times {10}^6}=3\times {10}^2$.

   $3\times {10}^2=300$ seconds.

   $300$ seconds