Use long division to convert 27/50 to a decimal.(1 point) Responses 27.5 27.5 0.54 0.54 5.4 5.4 1.851

Answer 1

To convert \( \frac{27}{50} \) to a decimal using long division, we can set it up as follows:

1. Determine how many times 50 goes into 27: Since 50 is greater than 27, it goes 0 times. Therefore, we place a decimal point and add a zero (making it 270).

2. Now, we try 50 into 270:

   • 50 goes into 270 a total of 5 times (since \( 50 \times 5 = 250 \)).
   • Write down 5 after the decimal point.

3. Subtract \( 250 \) from \( 270 \):

   • \( 270 - 250 = 20 \).

4. Bring down another zero (making it 200):

   • Now we determine how many times 50 goes into 200.
   • 50 goes into 200 a total of 4 times (since \( 50 \times 4 = 200 \)).
   • Write down 4.

5. Subtract \( 200 - 200 = 0 \).

Since we reached 0, we can stop here.

Putting it all together, we get \( 0.54 \).

The correct decimal representation of \( \frac{27}{50} \) is \( 0.54 \).

So the answer is 0.54.

Answer 2

Question Use long division to convert 3 3/8 to a decimal.(1 point) Responses 0.375 0.375 3.375 3.375 2.66 2.66 33.75 33.75

Answer 3

To convert the mixed number \( 3 \frac{3}{8} \) to a decimal, we'll first convert the fraction \( \frac{3}{8} \) into a decimal.

1. Perform long division for \( 3 \div 8 \):

   • 8 goes into 3 0 times. So we write down 0 and add a decimal point.
   • Now, we can work with 30 (by adding a zero after the decimal).
   • 8 goes into 30 3 times (since \( 8 \times 3 = 24 \)).
   • We write down 3 after the decimal, giving us \( 0.3 \).

2. Subtract \( 24 \) from \( 30 \):

   • \( 30 - 24 = 6 \).

3. Bring down another zero, making it 60.

   • 8 goes into 60 7 times (since \( 8 \times 7 = 56 \)).
   • Write down 7, giving us \( 0.37 \).

4. Subtract \( 56 \) from \( 60 \):

   • \( 60 - 56 = 4 \).

5. Bring down another zero, making it 40.

   • 8 goes into 40 5 times (since \( 8 \times 5 = 40 \)).
   • Write down 5, giving us \( 0.375 \).

6. Subtract \( 40 \) from \( 40 \):

   • \( 40 - 40 = 0 \), so we’ve finished converting.

Now, we add the whole number part (3) back to the decimal we found. Thus, \( 3 \frac{3}{8} = 3 + 0.375 = 3.375 \).

So the decimal representation of \( 3 \frac{3}{8} \) is 3.375.

Answer 4

Use long division to convert 4/15 to a decimal.(1 point) Responses ≈0.27 approximately equals 0.27 3.75 3.75 26 26 4.15

Answer 5

To convert \( \frac{4}{15} \) to a decimal using long division, we'll set it up as follows:

1. Set up the division: We're dividing 4 by 15. Since 15 is larger than 4, we can place a decimal point and add a zero, making it 40.

2. Now determine how many times 15 goes into 40:

   • 15 goes into 40 2 times (since \( 15 \times 2 = 30 \)).
   • Write down 2 after the decimal point.

3. Subtract \( 30 \) from \( 40 \):

   • \( 40 - 30 = 10 \).

4. Bring down another zero, making it 100:

   • Now determine how many times 15 goes into 100:
   • 15 goes into 100 6 times (since \( 15 \times 6 = 90 \)).
   • Write down 6 after the 2.

5. Subtract \( 90 \) from \( 100 \):

   • \( 100 - 90 = 10 \).

6. Repeat the process:

   • Bring down another zero to make it 100 again.
   • We already know that 15 goes into 100 6 times, leaving us with 10 again.

This process will continue to repeat, leading to a recurring decimal \( 0.26666...\) (with the 6 repeating).

For practical purposes, if we round \( 0.26666...\) to two decimal places, it is approximately \( 0.27 \).

Thus, the decimal representation of \( \frac{4}{15} \) is approximately 0.27.

Answer 6

Use long division to convert 7/11 to a decimal.(1 point) Responses ≈1.571428 approximately equals 1.571428 ≈0.63 approximately equals 0.63 7.11 7.11 63

Answer 7

To convert \( \frac{7}{11} \) to a decimal using long division, we follow these steps:

1. Set up the division: We are dividing \( 7 \) by \( 11 \). Since \( 11 \) is greater than \( 7 \), we can put a decimal point and add a zero, making it \( 70 \).

2. Determine how many times 11 goes into 70:

   • \( 11 \) goes into \( 70 \) a total of 6 times (since \( 11 \times 6 = 66 \)).
   • We write down \( 6 \).

3. Subtract \( 66 \) from \( 70 \):

   • \( 70 - 66 = 4 \).

4. Bring down another zero, making it \( 40 \):

   • Now, determine how many times \( 11 \) goes into \( 40 \):
   • \( 11 \) goes into \( 40 \) a total of 3 times (since \( 11 \times 3 = 33 \)).
   • Write down \( 3 \).

5. Subtract \( 33 \) from \( 40 \):

   • \( 40 - 33 = 7 \).

6. Bring down another zero, making it \( 70 \) again:

   • We repeat this process since \( 70 \) is the same as our first step. We already calculated that \( 11 \) goes into \( 70 \) 6 times.

So far, the division gives us \( 0.63 \) with a repeating pattern starting from \( 6 \).

Thus, when we combine all the parts, \( \frac{7}{11} \) converts to \( 0.636363...\) or \( 0.\overline{63} \).

Conclusion:

This indicates that \( \frac{7}{11} \) is approximately \( 0.63 \), leading us to the final answer:

The decimal representation of \( \frac{7}{11} \) is approximately 0.63.

However, since you mentioned only specific responses, the more precise and longer decimal representation for \( \frac{7}{11} \) is approximately 1.571428 (if computed as a mixed number, which doesn't apply in this case, it's purely \( 0.\overline{6363} \)). The possible responses don't identify this, suggesting a mistake in options. Choose 0.63 for simplicity if you need.

So, the appropriate response is \( \approx 0.63 \). If required more accurately, it's \( 0.636363...\).

Answer 8

Use long division to convert 5 3/16 to a decimal.(1 point) Responses 0.1875 0.1875 5.36 5.36 5.1875 5.1875 ≈5.3

Answer 9

To convert the mixed number \( 5 \frac{3}{16} \) to a decimal, we will first convert the fraction \( \frac{3}{16} \) into a decimal using long division.

Step 1: Convert \( \frac{3}{16} \) to a decimal.

1. Set up the division: We are dividing \( 3 \) by \( 16 \). Since \( 16 \) is greater than \( 3 \), we can place a decimal point and add a zero, making it \( 30 \).

2. Determine how many times \( 16 \) goes into \( 30 \):

   • \( 16 \) goes into \( 30 \) a total of 1 time (since \( 16 \times 1 = 16 \)).
   • Write \( 1 \) after the decimal point.

3. Subtract \( 16 \) from \( 30 \):

   • \( 30 - 16 = 14 \).

4. Bring down another zero, making it \( 140 \):

   • Now, determine how many times \( 16 \) goes into \( 140 \):
   • \( 16 \) goes into \( 140 \) a total of 8 times (since \( 16 \times 8 = 128 \)).
   • Write \( 8 \) after the \( 1 \).

5. Subtract \( 128 \) from \( 140 \):

   • \( 140 - 128 = 12 \).

6. Bring down another zero, making it \( 120 \):

   • \( 16 \) goes into \( 120 \) a total of 7 times (since \( 16 \times 7 = 112 \)).
   • Write \( 7 \) after the \( 18 \).

7. Subtract \( 112 \) from \( 120 \):

   • \( 120 - 112 = 8 \).

8. Bring down another zero, making it \( 80 \):

   • \( 16 \) goes into \( 80 \) a total of 5 times (since \( 16 \times 5 = 80 \)).
   • Write \( 5 \) after the \( 187 \).

9. Subtract \( 80 \) from \( 80 \) to get \( 0 \).

Putting it all together, we find that:

\[ \frac{3}{16} = 0.1875 \]

Step 2: Add the whole number part.

Now we add this decimal to the whole number part of the mixed number:

\[ 5 + 0.1875 = 5.1875 \]

Conclusion

Therefore, the decimal representation of \( 5 \frac{3}{16} \) is \( 5.1875 \).

So, the correct response is 5.1875.