7.4 Upper and lower bounds — Practise

1. H A length is $9.3$ cm to the nearest $0.1$ cm. Give its bounds.
2. H A rectangle has length $8.2$ cm and width $4.6$ cm, each to the nearest $0.1$ cm. Find the upper bound for its area.
3. H Using the same measurements, find the lower bound for the rectangle area.
4. H A distance is $100$ m to the nearest metre and a time is $8.0$ s to the nearest $0.1$ s. Find the upper bound for speed.
5. H For positive $a$ and $b$, which combination gives the greatest value of $a/b$: greatest $a$ with least $b$, or least $a$ with greatest $b$?
6. H A cube side is $3.0$ cm to the nearest $0.1$ cm. Find the upper bound for its volume.
7. H A mass is $50$ g to the nearest gram and volume is $20$ cm$^3$ to the nearest cm$^3$. Find the greatest possible density.
8. H Two lengths are $12.4$ cm and $8.1$ cm, each to the nearest $0.1$ cm. Find the upper bound for their difference.
9. H A speed is $v=d/t$ where $d=72$ km to the nearest km and $t=1.2$ h to the nearest $0.1$ h. Find the lower bound for speed.
10. H A rectangle has sides $5.0$ m and $2.0$ m, each to the nearest $0.1$ m. Find upper bounds for its perimeter and area.