using rational approximations, what statement is true ?

Question

a. 3 > √9
b. π > √9
c. 3 < √9
d. π < √9

Answer 1

To evaluate the options, we find the values of \(\sqrt{9}\) and \(\pi\):

1. \(\sqrt{9} = 3\)
2. \(\pi \approx 3.14\) (a well-known approximation of \(\pi\))

Now, let's analyze each option:

a. \(3 > \sqrt{9}\)
This is false because \(3 = \sqrt{9}\).

b. \(\pi > \sqrt{9}\)
This is true because \(3.14 > 3\).

c. \(3 < \sqrt{9}\)
This is false because \(3 = \sqrt{9}\).

d. \(\pi < \sqrt{9}\)
This is false because \(3.14 > 3\).

Thus, the true statement is:

b. \(\pi > \sqrt{9}\)

Answer 2

write 67.45 in expanded form.
a. (7 x 10) + (6 x 1) + (4 x 1/10) + (5 x 1/100)
b. (6 x 10) + (7 x 1) + (4 x 1/10) + (5 x 1/100)
c. (6 x 10) + (7 x 1) + (4 x 1/10^1) + (5 x 1/10^2)
d. (7 x 1) + (4 x 1/10) + (5 x 1/100)

Answer 3

To write the number 67.45 in expanded form, we can break it down into its place values. The number consists of:

• 6 in the tens place (60)
• 7 in the ones place (7)
• 4 in the tenths place (0.4)
• 5 in the hundredths place (0.05)

This can be expressed as:

\[ (6 \times 10) + (7 \times 1) + (4 \times \frac{1}{10}) + (5 \times \frac{1}{100}) \]

Now let's analyze the options:

a. \((7 \times 10) + (6 \times 1) + (4 \times \frac{1}{10}) + (5 \times \frac{1}{100})\)

• This is incorrect because the tens and ones are switched.

b. \((6 \times 10) + (7 \times 1) + (4 \times \frac{1}{10}) + (5 \times \frac{1}{100})\)

• This is correct.

c. \((6 \times 10) + (7 \times 1) + (4 \times \frac{1}{10^1}) + (5 \times \frac{1}{10^2})\)

• This is also correct because \(\frac{1}{10^1} = \frac{1}{10}\) and \(\frac{1}{10^2} = \frac{1}{100}\).

d. \((7 \times 1) + (4 \times \frac{1}{10}) + (5 \times \frac{1}{100})\)

• This is incorrect because it omits the tens place.

The correct answers are:

b. \((6 \times 10) + (7 \times 1) + (4 \times \frac{1}{10}) + (5 \times \frac{1}{100})\)

and also c. \((6 \times 10) + (7 \times 1) + (4 \times \frac{1}{10^1}) + (5 \times \frac{1}{10^2})\).

Answer 4

incorrect

Answer 5

I apologize for any confusion in my response. Let's correctly analyze the expanded form of the number 67.45.

The number 67.45 can be broken down as follows:

• The 6 is in the tens place, which represents \(6 \times 10 = 60\).
• The 7 is in the ones place, which represents \(7 \times 1 = 7\).
• The 4 is in the tenths place, which represents \(4 \times \frac{1}{10} = 0.4\).
• The 5 is in the hundredths place, which represents \(5 \times \frac{1}{100} = 0.05\).

So, in expanded form, \(67.45\) is:

\[ (6 \times 10) + (7 \times 1) + (4 \times \frac{1}{10}) + (5 \times \frac{1}{100}) \]

Now let's evaluate the choices provided:

a. \((7 \times 10) + (6 \times 1) + (4 \times \frac{1}{10}) + (5 \times \frac{1}{100})\)

• Incorrect (6 and 7 are interchanged).

b. \((6 \times 10) + (7 \times 1) + (4 \times \frac{1}{10}) + (5 \times \frac{1}{100})\)

• Correct.

c. \((6 \times 10) + (7 \times 1) + (4 \times \frac{1}{10^1}) + (5 \times \frac{1}{10^2})\)

• Also correct since \(\frac{1}{10^1} = \frac{1}{10}\) and \(\frac{1}{10^2} = \frac{1}{100}\).

d. \((7 \times 1) + (4 \times \frac{1}{10}) + (5 \times \frac{1}{100})\)

• Incorrect as it omits the tens place.

The correct choices for the expanded form of 67.45 are b and c. If you have additional context about why a specific option is considered incorrect, please share, and I'd be happy to clarify further!