Chapter 7: Measures, accuracy, standard form and surds

The chapter problem

A survey team records three measurements:

• a path on a map at scale $1:25\,000$ measures $3.2$ cm;
• a walker takes $10$ minutes to walk the path;
• a sample mass is $0.0042$ kg to 2 significant figures.

Work out the real length of the path in kilometres. Then work out the walker's average speed in km/h. Then write the range of values the sample mass could have, and write the recorded mass in standard form.

First contact: Pick one measurement you would convert or estimate first. You are not expected to solve the whole problem yet.

By the end of this chapter you will be able to

• convert metric units, use scales and read bearings;
• calculate speed, density and pressure;
• round values and write error intervals and bounds;
• calculate with standard form and surds.

Roadmap

1. 7.1 Units of measure and conversions
2. 7.2 Compound measures: speed, density and pressure
3. 7.3 Rounding and error intervals
4. 7.4 Upper and lower bounds
5. 7.5 Standard form
6. 7.6 Surds and exact calculations

At each Progress check, return to the survey measurements and decide which method now helps.

Your connection

Where have you or someone you know used a map scale, compared travel speeds, measured a quantity, or handled very large or small numbers? Write one example. You can return to it after studying the chapter.