Chapter 7: Review

The chapter problem, resolved

The map uses scale $1:25\,000$, and the path measures $3.2$ cm. Its real length is

The walker takes $10$ minutes, which is $1/6$ hour. The average speed is

A sample recorded as $0.0042$ kg to 2 significant figures lies from $0.00415$ kg up to, but not including, $0.00425$ kg. In standard form, the recorded value is $4.2\times10^{-3}$ kg. These steps show how conversion, compound measures, rounding and standard form connect.

Mixed practice: choose the method first

For each question, name the method before working.

1. Convert $2.7$ m to mm.
2. A cyclist travels $36$ km in $1.5$ hours. Find the average speed.
3. Write the interval for $5.6$ kg rounded to the nearest $0.1$ kg.
4. A length is $8.2$ cm and a width is $3.4$ cm, each to the nearest $0.1$ cm. Find the upper bound for the area.
5. Work out $(4\times10^6)(3\times10^{-2})$ in standard form.
6. Simplify $\sqrt{108}-\sqrt{12}$.
7. A map distance is $6$ cm at scale $1:50\,000$. Find the real distance in kilometres.
8. A force of $450$ N acts on $0.15\text{ m}^2$. Find the pressure.

What you can now do

• convert and compare measurements with units;
• use formulae for compound measures;
• interpret rounded values through intervals and bounds;
• work exactly with standard form and surds.

Your connection

Return to your example from the opening page. Which method from this chapter could help with it? Write one new connection you noticed while learning.