Using a number line, what whole number and rational number to the nearest half is 97−−√ between? (1point)
The number line can help us visualize the position of the square root of 97.
On the number line, we know that the square root of 97 is greater than 9 (since 9 squared equals 81), but less than 10 (since 10 squared equals 100).
To find the whole number nearest to √97, we use the concept of rounding. √97 is closer to 10 than to 9, so the whole number nearest to √97 is 10.
To find the rational number to the nearest half, we look at the fractional part of √97. We know that √97 is greater than the halfway point between 9 and 10, which is 9.5, but less than the halfway point between 10 and 11, which is 10.5. Therefore, the rational number nearest to √97 is 10.
In summary, the whole number nearest to √97 is 10, and the rational number nearest to √97 is also 10.
Using rational approximations, what is an inequality statement comparing 21−−√ and 17−−√? Enter <, >, or =.(1 point)
To compare 21−−√ and 17−−√ using rational approximations, we can convert these square roots into rational numbers.
The square root of 21 is approximately 4.58, while the square root of 17 is approximately 4.12.
Since 4.58 > 4.12, we can conclude that 21−−√ is greater than 17−−√.
Therefore, the inequality statement comparing 21−−√ and 17−−√ is 21−−√ > 17−−√.
Using rational approximations, what is an inequality statement comparing π and 8–√? Enter <, >, or =.(1 point)
To compare π and 8–√ using rational approximations, we can approximate π as 3.14 and simplify 8–√ as 2.83.
Since 3.14 > 2.83, we can conclude that π is greater than 8–√.
Therefore, the inequality statement comparing π and 8–√ is π > 8–√.
The bank balances of several people are as follows: $123.49, $75.23, −$123.69, $75.89, −$123.43. Which balance is the lowest? Give the answer in dollars.(1 point)
To determine the lowest bank balance, we compare the values given.
The bank balances are listed as follows:
$123.49, $75.23, −$123.69, $75.89, −$123.43.
From the given list, we can see that the lowest bank balance is −$123.69.
Therefore, the lowest bank balance is -$123.69.