**Topic**

a) Round the number 865 549 to hundreds. How accurate is the approximate number received?

b) Round the number -0.526 to the nearest hundredth. How accurate is the approximate number received?

**Solution method – See details**

Round numbers and calculate d

We say \(a\) is an approximation of \(\overline a \) with precision \(d\) if \({\Delta _a} = \left| {a – \overline a } \right| \le d\)

**Detailed explanation**

a) The rounded number of 865 549 to hundreds is 865 500

We have: \({\Delta _a} = \left| {865{\rm{ }}500 – 865{\rm{ }}549} \right| = 49 \le 50 = d\)

b) The rounded number of -0.526 to the hundredths is -0.53

We have: \({\Delta _a} = \left| { – 0.53 – \left( { – 0.526} \right)} \right| = 0.004 \le 0.005 = d\)