Bounds with decimal places and significant figures

Understanding Bounds

Bounds allow mathematical calculations to be more accurate. They determine the higher or lower limits (the smallest or largest possible values) of a rounded number.
A rounded or approximated number holds a range of values, the upper bound is the highest possible value and the lower bound is the least.
For example, the number 6.4 (rounded to one decimal place) has a lower bound of 6.35 and an upper bound of 6.45. This is because numbers from 6.35 to just less than 6.45 would be rounded to 6.4.

Decimal Places determine the value of the upper and lower bound of a rounded number.
If a number is rounded to one decimal place, the lower bound would be 0.05 less than the rounded number and the upper bound would be 0.05 more.
For example, a number rounded to 3.4 (to one decimal place) would have a lower bound of 3.35 and an upper bound of 3.45.
If a number is rounded to two decimal places, the bounds would be 0.005 less and more than the rounded number.

If a number is rounded to significant figures, the bounds would also consider the place value of the rounded figures.
When identifying bounds of a number rounded to significant figures, consider the next number in sequence after the last significant figure.
For example, a number rounded to 230 (to two significant figures) could be anything from 225 to 235 to be rounded to 230.

When working with a range of values, use the upper and lower bounds to provide the most accurate results.
If measurements are being added, use the upper bounds for each measurement to find the maximum total, and the lower bounds for each measurement to find the minimum total.
If calculations involving subtraction are made, the maximum difference will be achieved by subtracting the lower bound of the number being subtracted from the upper bound of the number it is being subtracted from.

Not considering the next value in sequence when identifying bounds for numbers rounded to significant figures.
Forgetting to adjust for the number of decimal places when identifying lower and upper bounds.
Misapplying bounds, especially in subtraction and addition problems.
Making errors when calculating the upper and lower bounds of multiple measurements.
Not understanding the purpose of bounds in increasing precision of mathematical operations.