Determine the Range of a Rounded Value
A number x rounds to value R if x is at least the midpoint below R and less than the midpoint above R. Working backwards from a rounded value determines the range of possible original values. This Grade 5 math skill from Eureka Math Chapter 3 covers place value and rounding decimal fractions including range analysis.
Key Concepts
A number $x$ rounds to a value $R$ if it is between the halfway point just below $R$ and the halfway point just above $R$. This means that if $x$ is at least the lower midpoint and less than the upper midpoint , it will round to $R$.
Common Questions
How do you find the range of numbers that round to a given value?
The minimum is the midpoint just below the rounded value (half a unit lower), and the maximum is the midpoint just above it (half a unit higher but not including it). Any number in that range rounds to the given value.
What numbers round to 8 when rounded to the nearest whole number?
Numbers from 7.5 up to but not including 8.5 round to 8. The range is 7.5 is less than or equal to x which is less than 8.5.
What is the range of numbers that round to 4.3 at the nearest tenth?
Numbers from 4.25 up to but not including 4.35 round to 4.3. The minimum is 4.25 and the range extends to just below 4.35.
Why is the upper boundary excluded from the range?
A number equal to the upper midpoint (like 8.5) rounds up to the next value (9), not down to 8, so it is excluded from the range of numbers that round to 8.