Round 0.9968 to 2 significant figures.
The Correct Answer and Explanation is:
To round the number 0.9968 to two significant figures, we first identify the significant figures in the number. Significant figures include all non-zero digits, any zeros between significant digits, and any trailing zeros in the decimal part.
In the number 0.9968, the significant figures are as follows:
- The “9” is significant.
- The second “9” is also significant.
- The “6” is significant.
- The “8” is significant.
This means the first four digits (9, 9, 6, and 8) are significant. However, since we are asked to round to two significant figures, we only focus on the first two digits, which are “9” and “9.”
Next, we need to determine whether we need to round the second significant figure. The next digit after the second significant figure (the third digit) is “6.” According to rounding rules, if this digit is 5 or greater, we round up the last significant figure by one. In this case, since “6” is greater than 5, we round the second “9” up to “10.”
However, rounding “9” up to “10” introduces a complication: it changes the first digit as well. Thus, instead of 0.99, we get 1.0. Therefore, the final rounded value becomes:
[ \text{Rounded Value} = 1.0 ]
It’s important to express the answer in a way that reflects the significant figures. Here, “1.0” indicates that the answer is precise to two significant figures, where the zero after the decimal point shows that the value is accurate to that level of precision.
In summary, rounding 0.9968 to two significant figures gives us 1.0.