Free · Roots and rounding
Round to Tens with Nine Tie Rules
Round signed decimals to a multiple of ten using all nine captured direction and exact tie rules.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
25 rounds to 30 with Half up.
10*((rounding_mode == 0) ? (sign((number / 10)) * ceilExact(abs((number / 10)))) : ((rounding_mode == 1) ? (sign((number / 10)) * floorExact(abs((number / 10)))) : ((rounding_mode == 2) ? ceilExact((number / 10)) : ((rounding_mode == 3) ? floorExact((number / 10)) : ((rounding_mode == 4) ? (sign((number / 10)) * floorExact(abs((number / 10)) + 0.5)) : ((rounding_mode == 5) ? ((isInteger(2 * (number / 10)) and not (isInteger((number / 10)))) ? (sign((number / 10)) * floorExact(abs((number / 10)))) : (sign((number / 10)) * floorExact(abs((number / 10)) + 0.5))) : ((rounding_mode == 6) ? ((isInteger(2 * (number / 10)) and not (isInteger((number / 10)))) ? (sign((number / 10)) * (floorExact(abs((number / 10))) + (isInteger(floorExact(abs((number / 10))) / 2) ? 0 : 1))) : (sign((number / 10)) * floorExact(abs((number / 10)) + 0.5))) : ((rounding_mode == 7) ? ((isInteger(2 * (number / 10)) and not (isInteger((number / 10)))) ? ceilExact((number / 10)) : (sign((number / 10)) * floorExact(abs((number / 10)) + 0.5))) : ((isInteger(2 * (number / 10)) and not (isInteger((number / 10)))) ? floorExact((number / 10)) : (sign((number / 10)) * floorExact(abs((number / 10)) + 0.5)))))))))))
Worked example
Enter these known values and leave the other values blank.
- Number
- 25
- Result
- 30
Assumptions and limitations
- Select among all nine direction and tie rules by showing the advanced modes.
- Decimal input is rounded directly; exact half-integers use the selected tie rule. The original positive upper input limit remains active.
Common questions
What does this calculate?
Select among all nine direction and tie rules by showing the advanced modes.
Can I solve backwards?
The captured output is forward only. Enter independent values; clearing or resetting preserves the selected controls.
References
Translate the nine captured rounding modes directly from the entered decimal to a multiple of ten. Exact decimal floor and half detection avoid the captured string reconstruction losing decimal fractions; preserve signed hidden components, all controls, and the original positive upper input limit, with quotient magnitude below 10^50.