To round the number 35.980 to 3 significant figures, we'll follow a step-by-step process:
1. Identify the first three significant figures:
The significant figures are the meaningful digits in a number. In 35.980, the first three significant figures are 3, 5, and 9.
2. Consider the place of the third significant figure:
In this number, the third significant figure (9) is in the tenths place.
3. Look at the digit immediately following those three significant figures:
In the number 35.980, the digit immediately following the third significant figure (9) is an 8. This is important because it will determine whether we round up or down.
4. Apply rounding rules:
- If the digit following the last significant figure is 5 or greater, we round up the last significant figure.
- If the digit is less than 5, we leave the last significant figure as it is.
Since the digit following the third significant figure (9) is an 8 (which is greater than 5), we round up the 9 in 35.9 to 10. This increment causes the whole number to round up.
5. Reconstruct the number with the rounded value:
After rounding up, the number 35.9 becomes 36 when rounded to three significant figures.
So, when 35.980 is rounded to 3 significant figures, the result is:
[tex]\[ \boxed{36.0} \][/tex]
