Question

which is the best estimate of \\(\sqrt{0.96}\\) to the nearest hundredth?\
\\(\bigcirc\\) 0.96\
\\(\bigcirc\\) 0.97\
\\(\bigcirc\\) 0.98\
\\(\bigcirc\\) 1.00

Explanation:

Step1: Calculate the square root of 0.96

We know that to find the square root of a number, we can use a calculator or recall the properties of square roots. Using a calculator, we calculate $\sqrt{0.96}$.
$\sqrt{0.96} \approx 0.9798$

Step2: Round to the nearest hundredth

To round to the nearest hundredth, we look at the thousandth place. The number in the thousandth place of 0.9798 is 9. Since 9 > 5, we round up the hundredth place.
So, 0.9798 rounded to the nearest hundredth is 0.98? Wait, no, wait. Wait, 0.9798: the hundredth place is 7, the thousandth is 9. So when rounding to the nearest hundredth, we look at the thousandth digit (9). Since 9 ≥ 5, we add 1 to the hundredth digit. So 7 + 1 = 8? Wait, no, 0.9798: let's write it as 0.97 (hundredth place) and then the next digit is 9. So 0.97 + 0.01 = 0.98? Wait, no, wait, 0.9798 is approximately 0.98 when rounded to the nearest hundredth? Wait, no, wait, 0.9798: the first decimal is 9 (tenths), second is 7 (hundredths), third is 9 (thousandths), fourth is 8 (ten - thousandths). When rounding to the nearest hundredth, we look at the thousandth digit (9). Since 9 ≥ 5, we round up the hundredth digit. So 7 becomes 8, so 0.98. But wait, let's check with a calculator. Wait, actually, $\sqrt{0.96}\approx0.9798$, which is approximately 0.98 when rounded to the nearest hundredth? Wait, no, wait, 0.9798 is closer to 0.98? Wait, no, 0.9798: the hundredth place is 7, the thousandth is 9. So 0.97 + 0.01 = 0.98? Wait, but let's check the options. The options are 0.96, 0.97, 0.98, 1.00. Wait, maybe I made a mistake. Wait, let's calculate $0.98^2 = 0.9604$, and $0.97^2=0.9409$, $0.96^2 = 0.9216$, $1.00^2 = 1$. Now, 0.96 is between $0.97^2 = 0.9409$ and $0.98^2=0.9604$. Now, 0.96 - 0.9409 = 0.0191, and 0.9604 - 0.96 = 0.0004. So 0.96 is much closer to $0.98^2$ (since 0.0004 is much smaller than 0.0191). Wait, no, $0.98^2 = 0.9604$, which is 0.0004 more than 0.96. And $0.97^2=0.9409$, which is 0.0191 less than 0.96. So $\sqrt{0.96}$ is closer to 0.98? Wait, but when we calculate $\sqrt{0.96}\approx0.9798$, which is approximately 0.98 when rounded to the nearest hundredth. But wait, the option 0.98 is there. But wait, let's check again. Wait, 0.9798 rounded to the nearest hundredth: the third decimal is 9, so we round up the second decimal. So 7 becomes 8, so 0.98. So the best estimate is 0.98? But wait, let's check the options. Wait, but maybe I made a mistake. Wait, $0.98^2 = 0.9604$, which is very close to 0.96. So $\sqrt{0.96}\approx0.9798\approx0.98$ when rounded to the nearest hundredth. So the answer should be 0.98.

Answer:

C. 0.98 (assuming the options are labeled as A. 0.96, B. 0.97, C. 0.98, D. 1.00)