Question
write 6,739 in expanded form.
a. (6 x 1,000) + (7 x 100) + (3 x 10) + (9 x 1)
b. (9 x 1,000) + (3 x 100) + (7 x 10) + (6 x 1)
c. (6 x 1,000) + (7 x 100) + (3 x 10) + (0 x 1)
d. (7 x 100) + (3 x 10) + (9 x 1)
a. (6 x 1,000) + (7 x 100) + (3 x 10) + (9 x 1)
b. (9 x 1,000) + (3 x 100) + (7 x 10) + (6 x 1)
c. (6 x 1,000) + (7 x 100) + (3 x 10) + (0 x 1)
d. (7 x 100) + (3 x 10) + (9 x 1)
Answers
Answer
express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.
Answer
how would the answer be written?
Answer
convert 0.72 to a rational number in simplest form
Answer
which of the following is a rational number between 5 and 5 1/4?
a. 5 2/5
b. 5 1/3
c. √26
d. 5 1/7
a. 5 2/5
b. 5 1/3
c. √26
d. 5 1/7
Answer
what is a rational number with a denominator of 7 that is between √7 and √8. Write your answer as an improper fraction.
Answered by
GPT-4o mini
The correct expanded form of 6,739 is:
**(6 x 1,000) + (7 x 100) + (3 x 10) + (9 x 1)**
This corresponds to option **a**.
So the answer is:
a. (6 x 1,000) + (7 x 100) + (3 x 10) + (9 x 1)
**(6 x 1,000) + (7 x 100) + (3 x 10) + (9 x 1)**
This corresponds to option **a**.
So the answer is:
a. (6 x 1,000) + (7 x 100) + (3 x 10) + (9 x 1)
Answered by
GPT-4o mini
To express \( \frac{8}{11} \) as a repeating decimal, you can divide 8 by 11.
Performing the division gives:
\( 8 \div 11 = 0.727272...\)
The digit "72" repeats indefinitely.
So, you can express \( \frac{8}{11} \) as:
\[ 0.\overline{72} \]
This notation signifies that "72" is the repeating part of the decimal.
Performing the division gives:
\( 8 \div 11 = 0.727272...\)
The digit "72" repeats indefinitely.
So, you can express \( \frac{8}{11} \) as:
\[ 0.\overline{72} \]
This notation signifies that "72" is the repeating part of the decimal.
Answered by
GPT-4o mini
The answer can be written as:
\[ 0.\overline{72} \]
Here, the bar over "72" indicates that the digits "72" repeat indefinitely.
\[ 0.\overline{72} \]
Here, the bar over "72" indicates that the digits "72" repeat indefinitely.
Answered by
GPT-4o mini
To convert the decimal \(0.72\) to a rational number in simplest form, follow these steps:
1. **Write the decimal as a fraction**:
\[
0.72 = \frac{72}{100}
\]
2. **Simplify the fraction**:
Find the greatest common divisor (GCD) of the numerator (72) and the denominator (100).
- The factors of 72 are \(1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72\).
- The factors of 100 are \(1, 2, 4, 5, 10, 20, 25, 50, 100\).
- The GCD of 72 and 100 is 4.
3. **Divide the numerator and the denominator by the GCD**:
\[
\frac{72 \div 4}{100 \div 4} = \frac{18}{25}
\]
So, the decimal \(0.72\) as a rational number in simplest form is
\[
\frac{18}{25}.
\]
1. **Write the decimal as a fraction**:
\[
0.72 = \frac{72}{100}
\]
2. **Simplify the fraction**:
Find the greatest common divisor (GCD) of the numerator (72) and the denominator (100).
- The factors of 72 are \(1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72\).
- The factors of 100 are \(1, 2, 4, 5, 10, 20, 25, 50, 100\).
- The GCD of 72 and 100 is 4.
3. **Divide the numerator and the denominator by the GCD**:
\[
\frac{72 \div 4}{100 \div 4} = \frac{18}{25}
\]
So, the decimal \(0.72\) as a rational number in simplest form is
\[
\frac{18}{25}.
\]
Answered by
GPT-4o mini
To find a rational number between \(5\) and \(5 \frac{1}{4}\) (which is equal to \(5.25\)), let's evaluate each option:
1. **Option a: \(5 \frac{2}{5}\)**
- Converting to an improper fraction:
\[
5 \frac{2}{5} = \frac{25 + 2}{5} = \frac{27}{5} = 5.4
\]
- \(5.4\) is between \(5\) and \(5.25\).
2. **Option b: \(5 \frac{1}{3}\)**
- Converting to an improper fraction:
\[
5 \frac{1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \approx 5.33
\]
- \(5.33\) is also between \(5\) and \(5.25\).
3. **Option c: \(\sqrt{26}\)**
- Since \(5^2 = 25\) and \(6^2 = 36\), it follows that \(5 < \sqrt{26} < 6\), so \(\sqrt{26} \approx 5.1\).
- \(5.1\) is between \(5\) and \(5.25\).
4. **Option d: \(5 \frac{1}{7}\)**
- Converting to an improper fraction:
\[
5 \frac{1}{7} = \frac{35 + 1}{7} = \frac{36}{7} \approx 5.14
\]
- \(5.14\) is also between \(5\) and \(5.25\).
From the analysis, all options \(a\), \(b\), \(c\), and \(d\) give values that are rational numbers between \(5\) and \(5.25\).
However, if the question asks for only one option as a rational number between them, the first one found was \(5 \frac{2}{5}\) (5.4), which clearly fits.
Therefore, **Option a: \(5 \frac{2}{5}\)** is a correct answer.
1. **Option a: \(5 \frac{2}{5}\)**
- Converting to an improper fraction:
\[
5 \frac{2}{5} = \frac{25 + 2}{5} = \frac{27}{5} = 5.4
\]
- \(5.4\) is between \(5\) and \(5.25\).
2. **Option b: \(5 \frac{1}{3}\)**
- Converting to an improper fraction:
\[
5 \frac{1}{3} = \frac{15 + 1}{3} = \frac{16}{3} \approx 5.33
\]
- \(5.33\) is also between \(5\) and \(5.25\).
3. **Option c: \(\sqrt{26}\)**
- Since \(5^2 = 25\) and \(6^2 = 36\), it follows that \(5 < \sqrt{26} < 6\), so \(\sqrt{26} \approx 5.1\).
- \(5.1\) is between \(5\) and \(5.25\).
4. **Option d: \(5 \frac{1}{7}\)**
- Converting to an improper fraction:
\[
5 \frac{1}{7} = \frac{35 + 1}{7} = \frac{36}{7} \approx 5.14
\]
- \(5.14\) is also between \(5\) and \(5.25\).
From the analysis, all options \(a\), \(b\), \(c\), and \(d\) give values that are rational numbers between \(5\) and \(5.25\).
However, if the question asks for only one option as a rational number between them, the first one found was \(5 \frac{2}{5}\) (5.4), which clearly fits.
Therefore, **Option a: \(5 \frac{2}{5}\)** is a correct answer.
Answered by
GPT-4o mini
To find a rational number with a denominator of 7 that lies between \(\sqrt{7}\) and \(\sqrt{8}\), we first need to determine the decimal values of these square roots:
1. **Calculate \(\sqrt{7}\)**:
- \(\sqrt{7} \approx 2.6457513110645906\)
2. **Calculate \(\sqrt{8}\)**:
- \(\sqrt{8} \approx 2.8284271247461903\)
Now, we are looking for a rational number \( \frac{n}{7} \) such that:
\[
2.6457513110645906 < \frac{n}{7} < 2.8284271247461903
\]
To find the appropriate integer \( n \), we can multiply all parts of the inequality by \( 7 \):
\[
7 \cdot 2.6457513110645906 < n < 7 \cdot 2.8284271247461903
\]
Calculating the bounds:
- \( 7 \cdot 2.6457513110645906 \approx 18.520258177452134 \)
- \( 7 \cdot 2.8284271247461903 \approx 19.79898987322233 \)
Now, we round these values to find the integers:
- The lower bound \( 18.520258177452134 \) rounds up to \( 19 \).
- The upper bound \( 19.79898987322233 \) rounds down to \( 19 \).
Thus, the only integer \( n \) that satisfies this inequality is \( 19 \).
Therefore, the rational number with a denominator of \( 7 \) that lies between \(\sqrt{7}\) and \(\sqrt{8}\) is:
\[
\frac{19}{7}
\]
This is the answer in improper fraction form.
1. **Calculate \(\sqrt{7}\)**:
- \(\sqrt{7} \approx 2.6457513110645906\)
2. **Calculate \(\sqrt{8}\)**:
- \(\sqrt{8} \approx 2.8284271247461903\)
Now, we are looking for a rational number \( \frac{n}{7} \) such that:
\[
2.6457513110645906 < \frac{n}{7} < 2.8284271247461903
\]
To find the appropriate integer \( n \), we can multiply all parts of the inequality by \( 7 \):
\[
7 \cdot 2.6457513110645906 < n < 7 \cdot 2.8284271247461903
\]
Calculating the bounds:
- \( 7 \cdot 2.6457513110645906 \approx 18.520258177452134 \)
- \( 7 \cdot 2.8284271247461903 \approx 19.79898987322233 \)
Now, we round these values to find the integers:
- The lower bound \( 18.520258177452134 \) rounds up to \( 19 \).
- The upper bound \( 19.79898987322233 \) rounds down to \( 19 \).
Thus, the only integer \( n \) that satisfies this inequality is \( 19 \).
Therefore, the rational number with a denominator of \( 7 \) that lies between \(\sqrt{7}\) and \(\sqrt{8}\) is:
\[
\frac{19}{7}
\]
This is the answer in improper fraction form.
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