Understanding Bounds and Rounding
When you see a rounded number, it's like seeing the tip of an iceberg - there's more underneath! Every rounded value has upper and lower bounds that show the range of possible original values.
The key rule is simple: take half of whatever unit the number was rounded to. For instance, if something's rounded to the nearest 100, you use ±50. Add this to get the upper bound, subtract it for the lower bound.
Here's your quick reference for different types of rounding:
- Nearest 1000: use ±500
- Nearest 100: use ±50
- Nearest 10: use ±5
- Nearest whole number: use ±0.5
- 1 decimal place: use ±0.05
- 2 decimal places: use ±0.005
💡 Quick tip: The more decimal places, the more precise the measurement - and the smaller your bounds become!
When you're doing calculations with rounded numbers, you need to consider how the bounds combine. For addition and subtraction, it's straightforward: max + max gives you the maximum result, whilst min + min gives the minimum.
But multiplication and division get trickier. For division especially, remember that dividing by the smallest possible value gives you the largest result - that's why max A ÷ min B gives you the maximum quotient.