Measurement and time-scale applications

1. Write 3.5 km in metres using scientific notation.

   2 marks
2. Write 0.0042 m in millimetres.

   2 marks
3. A particle is $2.5\times {10}^{-6}$ m wide. Express its width in micrometres.

   2 marks
4. A beam travels $1.8\times {10}^6$ m in $6\times {10}^{-3}$ s. Find its constant speed.

   3 marks
5. A model is 15 cm long and represents a real object 30 m long. Find the scale factor from real object to model.

   3 marks
6. A sensor records $2\times {10}^4$ readings each second. How many readings does it record in 5 minutes?

   3 marks

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

1. Write 3.5 km in metres using scientific notation.

   2 marks

   $1$ km $={10}^3$ m, so multiply 3.5 by ${10}^3$.

   $3.5\times {10}^3$ m
2. Write 0.0042 m in millimetres.

   2 marks

   $1$ m $=1000$ mm.

   $0.0042\times 1000=4.2$.

   $4.2$ mm
3. A particle is $2.5\times {10}^{-6}$ m wide. Express its width in micrometres.

   2 marks

   $1$ micrometre $={10}^{-6}$ m.

   Divide $2.5\times {10}^{-6}$ m by ${10}^{-6}$ m per micrometre.

   $2.5$ micrometres
4. A beam travels $1.8\times {10}^6$ m in $6\times {10}^{-3}$ s. Find its constant speed.

   3 marks

   $v=d÷t=\frac{1.8}{6}\times {10}^{6-\left(-3\right)}=0.3\times {10}^9$.

   Normalise to $3\times {10}^8$ m/s.

   $3\times {10}^8$ m/s
5. A model is 15 cm long and represents a real object 30 m long. Find the scale factor from real object to model.

   3 marks

   Convert 30 m to 3000 cm.

   $15÷3000=\frac{1}{200}$.

   $\frac{1}{200}$
6. A sensor records $2\times {10}^4$ readings each second. How many readings does it record in 5 minutes?

   3 marks

   $5$ minutes $=300=3\times {10}^2$ seconds.

   $\left(2\times {10}^4\right)\left(3\times {10}^2\right)=6\times {10}^6$.

   $6\times {10}^6$ readings