Sig Figs & Scientific Notation Helper (Grades 8–12)
Type a measurement. Roji marks which digits count, rounds to the right precision and names the rule it used, so you can do the next one yourself.
These are example numbers, not yours. Type over them, or start with empty boxes.
Your number
Round to
Your numbers
Exact is for numbers you counted (12 eggs) or that are defined (100 cm in 1 m). They never limit the sig figs.
Keys your keyboard may hide
Scientific notation can be typed as 4.5 x 10^-3 or 4.5e-3. Leave units off.
Options
When the digit you drop is exactly 5
Most classes round a 5 up. Some chemistry books round an exact 5 to the even digit. Use the rule your teacher uses.
Try an example
The five sig fig rules
- Digits 1 to 9 always count.
348has 3. - Zeros between non-zero digits count.
4.05has 3. - Zeros in front never count. They only hold the decimal point in place.
0.0045has 2. - Zeros at the end count when there is a decimal point.
4.50has 3, and100.0has 4. - Zeros at the end of a whole number are unclear.
1200could have 2, 3 or 4. Most classes say 2. Write1.20 × 103to show 3.
The two rules for calculating
- Multiplying and dividing: the answer keeps as many sig figs as the number with the fewest sig figs.
- Adding and subtracting: the answer stops at the last decimal place every number has. Count places here, not sig figs.
- Exact numbers (counted, or defined like 100 cm = 1 m) never limit the answer.
- More than one step: keep the extra digits until the end, then round once. Rounding early can change the answer.
Why do sig figs matter?
Every measurement has a last digit that was estimated. Sig figs tell a reader how precise your tool was. A ruler marked in millimeters can’t give a length to a thousandth of a millimeter, so an answer worked out from it shouldn’t look that precise either.
A calculator shows every digit it has room for. It doesn’t know which ones you measured. Deciding where to stop is your job.