Question

How do you round $ 100.1^\circ C $ to $ 1 $ significant figure?

Answer 1

Hint :The number of significant figures in $ 100.1^\circ C $ is four. Here, we should round the least significant digit first.In a number, significant figures are those digits which contribute to the precision of that number.

Complete Step By Step Answer:
Rules to follow when determining the number of significant figures in a number are given below.
- All non-zero digits of a number are considered to be significant.
- Any zeros between two significant digits are significant.
- Zeros before non-zero numbers are not significant.
- Trailing zeros to the right of the decimal are significant.
- Trailing zeros of a whole number with the decimal shown are significant.
- Trailing zeros of a whole number with no decimal shown are not significant.
Using these rules, we observe that in $ 100.1 $ , the first digit 1 is significant and the last digit 1 is also significant, as they are non-zero. Also, any zeros between two significant figures are also significant. Using this, we can say that the two zeros are also significant. So, the total number of significant digits in $ 100.1 $ is four.
Now, we have to round $ 100.1 $ to one significant figure. So, first let us round the least significant digit. Here, it is the tenths place value which has the digit 1. Since, 1 is less than 5 we round $ 100.1 $ to $ 100 $ . Now, $ 100 $ , $ 1 $ is significant, as it is not a zero. But the trailing two zeros of this whole number $ 100 $ are not significant. So, the number of significant figures in $ 100 $ is one.
Hence, $ 100.1^\circ C $ is rounded to $ 100^\circ C $ with $ 1 $ significant figure.

Note :
It is very much important to look at various different examples to understand these rules better. Here, note that when rounded off to one’s digit, the decimal point should not be considered. If mistakenly, you consider this, then the trailing two zeros will be considered to be significant.