Question
Consider the following decimal expansions.
7/999 = 0.007
59/999 = 0.059
1 388/999 = 1.388
Use the pattern above to determine which fraction is correctly converted into its decimal equivalent
A. 48/999 = 0.048
B. 4 772/999 = 4.772
C. 5/999 = 0.0005
D. 5 76/999 = 5.076
7/999 = 0.007
59/999 = 0.059
1 388/999 = 1.388
Use the pattern above to determine which fraction is correctly converted into its decimal equivalent
A. 48/999 = 0.048
B. 4 772/999 = 4.772
C. 5/999 = 0.0005
D. 5 76/999 = 5.076
Answers
Answered by
GPT-4o mini
To determine which fraction is correctly converted into its decimal equivalent, we can evaluate each option:
A. \( \frac{48}{999} \):
- This fraction can be simplified to \( 0.048 \).
B. \( \frac{4,772}{999} \):
- This fraction gives a decimal equivalent of \( 4.772 \).
C. \( \frac{5}{999} \):
- This fraction equals \( 0.005 \), not \( 0.0005 \).
D. \( \frac{5,76}{999} \):
- This fraction would be \( 5.076 \).
Now we can analyze the decimal expansions in context of the pattern observed with other fractions:
1. \( \frac{7}{999} = 0.007 \) corresponds to a fraction with a single digit (7) gives three decimal places.
2. \( \frac{59}{999} = 0.059 \) corresponds to a two-digit decimal giving three decimal places.
3. \( \frac{1,388}{999} = 1.388 \) corresponds to a four-digit numerator giving three digits before the decimal point and three decimal places.
Now let's check with our options:
A. \( \frac{48}{999} = 0.048 \) is consistent.
B. \( \frac{4,772}{999} = 4.772 \) is also consistent.
C. \( \frac{5}{999} \) should be \( 0.005 \) but is incorrectly stated as \( 0.0005 \), so it's inconsistent.
D. \( \frac{5,76}{999} = 5.076 \) is consistent.
Thus, A, B, and D are correct, but since we must choose one, the clear choice from your original statement is B:
**B. \( \frac{4,772}{999} = 4.772 \)**
A. \( \frac{48}{999} \):
- This fraction can be simplified to \( 0.048 \).
B. \( \frac{4,772}{999} \):
- This fraction gives a decimal equivalent of \( 4.772 \).
C. \( \frac{5}{999} \):
- This fraction equals \( 0.005 \), not \( 0.0005 \).
D. \( \frac{5,76}{999} \):
- This fraction would be \( 5.076 \).
Now we can analyze the decimal expansions in context of the pattern observed with other fractions:
1. \( \frac{7}{999} = 0.007 \) corresponds to a fraction with a single digit (7) gives three decimal places.
2. \( \frac{59}{999} = 0.059 \) corresponds to a two-digit decimal giving three decimal places.
3. \( \frac{1,388}{999} = 1.388 \) corresponds to a four-digit numerator giving three digits before the decimal point and three decimal places.
Now let's check with our options:
A. \( \frac{48}{999} = 0.048 \) is consistent.
B. \( \frac{4,772}{999} = 4.772 \) is also consistent.
C. \( \frac{5}{999} \) should be \( 0.005 \) but is incorrectly stated as \( 0.0005 \), so it's inconsistent.
D. \( \frac{5,76}{999} = 5.076 \) is consistent.
Thus, A, B, and D are correct, but since we must choose one, the clear choice from your original statement is B:
**B. \( \frac{4,772}{999} = 4.772 \)**
Answer
What is the fraction form of the following decimal expansion?
4.372
4.372
Answered by
GPT-4o mini
To convert the decimal \(4.372\) into fraction form, we can follow these steps:
1. **Separate the whole number from the decimal:**
\[
4.372 = 4 + 0.372
\]
2. **Convert the decimal part \(0.372\) into a fraction:**
- The decimal \(0.372\) can be expressed as:
\[
0.372 = \frac{372}{1000}
\]
This is because there are three digits after the decimal point.
3. **Simplify the fraction:**
- To simplify \(\frac{372}{1000}\), we must find the greatest common divisor (GCD) of \(372\) and \(1000\).
- The prime factorization of \(372\) is:
\[
372 = 2^2 \times 3 \times 31
\]
- The prime factorization of \(1000\) is:
\[
1000 = 2^3 \times 5^3
\]
- The GCD is \(4\) (the common factor is \(2^2\)).
- Now we simplify:
\[
\frac{372 \div 4}{1000 \div 4} = \frac{93}{250}
\]
4. **Combine the whole number and the fractional part:**
- The whole number \(4\) can be expressed as a fraction with the same denominator:
\[
4 = \frac{4 \times 250}{250} = \frac{1000}{250}
\]
- Now add the two fractions:
\[
4.372 = 4 + 0.372 = \frac{1000}{250} + \frac{93}{250} = \frac{1000 + 93}{250} = \frac{1093}{250}
\]
Thus, the decimal \(4.372\) in fraction form is:
\[
\frac{1093}{250}
\]
1. **Separate the whole number from the decimal:**
\[
4.372 = 4 + 0.372
\]
2. **Convert the decimal part \(0.372\) into a fraction:**
- The decimal \(0.372\) can be expressed as:
\[
0.372 = \frac{372}{1000}
\]
This is because there are three digits after the decimal point.
3. **Simplify the fraction:**
- To simplify \(\frac{372}{1000}\), we must find the greatest common divisor (GCD) of \(372\) and \(1000\).
- The prime factorization of \(372\) is:
\[
372 = 2^2 \times 3 \times 31
\]
- The prime factorization of \(1000\) is:
\[
1000 = 2^3 \times 5^3
\]
- The GCD is \(4\) (the common factor is \(2^2\)).
- Now we simplify:
\[
\frac{372 \div 4}{1000 \div 4} = \frac{93}{250}
\]
4. **Combine the whole number and the fractional part:**
- The whole number \(4\) can be expressed as a fraction with the same denominator:
\[
4 = \frac{4 \times 250}{250} = \frac{1000}{250}
\]
- Now add the two fractions:
\[
4.372 = 4 + 0.372 = \frac{1000}{250} + \frac{93}{250} = \frac{1000 + 93}{250} = \frac{1093}{250}
\]
Thus, the decimal \(4.372\) in fraction form is:
\[
\frac{1093}{250}
\]