Use long division to convert 27/50 to a decimal.(1 point)

Question

Responses

27.5
27.5

1.851
1.851

5.4
5.4

0.54

Answer 1

To convert \( \frac{27}{50} \) to a decimal using long division, we divide 27 by 50.

1. Place 27 under the long division bar and 50 outside.
2. Since 50 cannot go into 27, we add a decimal point and a zero to the 27, making it 270.
3. Determine how many times 50 can fit into 270. It fits 5 times (because \( 50 \times 5 = 250 \)).
4. Subtract 250 from 270, which leaves us with 20.
5. Bring down another 0, making it 200.
6. Now, determine how many times 50 fits into 200. It fits exactly 4 times (because \( 50 \times 4 = 200 \)).
7. Subtract 200 from 200, which leaves us with 0.

Putting it all together, \( \frac{27}{50} = 0.54 \).

So the correct answer is:

0.54

Answer 2

Use long division to convert 3 3/8 to a decimal.(1 point)
Responses

2.66
2.66

3.375
3.375

33.75
33.75

0.375

Answer 3

To convert \( 3 \frac{3}{8} \) to a decimal, we first convert the mixed number to an improper fraction and then divide.

1. Convert the mixed number to an improper fraction: \[ 3 \frac{3}{8} = \frac{(3 \times 8) + 3}{8} = \frac{24 + 3}{8} = \frac{27}{8} \]

2. Now, use long division to divide 27 by 8.

   • \( 8 \) goes into \( 27 \) three times (because \( 8 \times 3 = 24 \)).
   • Subtract \( 24 \) from \( 27 \), leaving \( 3 \).
   • Add a decimal point and a zero, making it \( 30 \).
   • \( 8 \) goes into \( 30 \) three times (because \( 8 \times 3 = 24 \)).
   • Subtract \( 24 \) from \( 30 \), leaving \( 6 \).
   • Add another zero, making it \( 60 \).
   • \( 8 \) goes into \( 60 \) seven times (because \( 8 \times 7 = 56 \)).
   • Subtract \( 56 \) from \( 60 \), leaving \( 4 \).
   • Add another zero, making it \( 40 \).
   • \( 8 \) goes into \( 40 \) five times (because \( 8 \times 5 = 40 \)).
   • Subtract \( 40 \) from \( 40 \) to get \( 0 \).

Putting this together:

• The result of the long division is \( 3.375 \).

Thus, 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

26
26

3.75
3.75

4.15

Answer 5

To convert \( \frac{4}{15} \) to a decimal using long division, we can follow these steps:

1. Set up the division: We are dividing 4 by 15, which is \( 4 \div 15 \).

2. Since 15 does not go into 4, we will place a decimal point and add a zero, treating it as 40.

   • Now, we have \( 15 \) into \( 40 \).

3. Determine how many times 15 fits into 40:

   • \( 15 \) goes into \( 40 \) two times (because \( 15 \times 2 = 30 \)).
   • Subtract \( 30 \) from \( 40 \) to get \( 10 \).

4. Bring down another zero making it \( 100 \).

5. Now divide again:

   • \( 15 \) goes into \( 100 \) six times (because \( 15 \times 6 = 90 \)).
   • Subtract \( 90 \) from \( 100 \) to get \( 10 \) again.

6. Bring down another zero making it \( 100 \) again.

7. Repeat the process:

   • Again, \( 15 \) goes into \( 100 \) six times (because \( 15 \times 6 = 90 \)).
   • Subtract \( 90 \) from \( 100 \) to get \( 10 \).

This means we will continuously get \( 0.2666...\) (with the 6 repeating).

Thus, \( \frac{4}{15} \approx 0.27 \) if rounded to two decimal places.

Therefore, the correct answer is:

≈0.27 (approximately equals 0.27)

Answer 6

Use long division to convert 7/11 to a decimal.(1 point)
Responses

≈1.571428
approximately equals 1.571428

63
63

7.11
7.11

≈0.63

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, which is \( 7 \div 11 \).

2. Since 11 does not go into 7, we will place a decimal point and add a zero, treating it as \( 70 \).

   • Now, we have \( 11 \) into \( 70 \).

3. Determine how many times 11 fits into 70:

   • \( 11 \) goes into \( 70 \) six times (because \( 11 \times 6 = 66 \)).
   • Subtract \( 66 \) from \( 70 \) to get \( 4 \).

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

5. Now divide again:

   • \( 11 \) goes into \( 40 \) three times (because \( 11 \times 3 = 33 \)).
   • Subtract \( 33 \) from \( 40 \) to get \( 7 \).

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

7. Repeat the process:

   • \( 11 \) goes into \( 70 \) six times again (because \( 11 \times 6 = 66 \)).
   • Subtract \( 66 \) from \( 70 \) to get \( 4 \).
   • Bring down another zero, making it \( 40 \).
   • \( 11 \) goes into \( 40 \) three times again (because \( 11 \times 3 = 33 \)).
   • Subtract \( 33 \) from \( 40 \) to get \( 7 \) again.

The decimals will continue to repeat with the pattern: \( 0.636363...\).

Putting this all together, we find that:

\[ \frac{7}{11} \approx 0.636363... \]

However, the equivalent decimal can also be expressed as \( \approx 0.636 \) when rounded or noted for its repeating nature.

In this case, among the options provided, the closest response that reflects a decimal representation is:

≈0.63 (approximately equals 0.63).

Answer 8

Use long division to convert 5 3/16 to a decimal.(1 point)
Responses

5.1875
5.1875

0.1875
0.1875

≈5.3
approximately equals 5.3

5.36

Answer 9

To convert \( 5 \frac{3}{16} \) to a decimal, we'll first convert the mixed number to an improper fraction and then perform long division.

1. Convert the mixed number to an improper fraction:

   \[ 5 \frac{3}{16} = \frac{(5 \times 16) + 3}{16} = \frac{80 + 3}{16} = \frac{83}{16} \]

2. Now use long division to divide 83 by 16.

   • Set up the division: \( 16 \) goes into \( 83 \).
   • Determine how many times \( 16 \) fits into \( 83 \):
     • \( 16 \times 5 = 80 \), so it fits 5 times.
   • Subtract \( 80 \) from \( 83\):
     • \( 83 - 80 = 3 \).
   • Now we have \( 3 \) left over. To continue dividing, we add a decimal point and a zero, bringing it to \( 30 \).

3. Continue the division:

   • Determine how many times \( 16 \) fits into \( 30 \):
     • \( 16 \) goes into \( 30 \) once (since \( 16 \times 1 = 16 \)).
   • Subtract \( 16 \) from \( 30\):
     • \( 30 - 16 = 14 \).
   • Bring down another zero to make it \( 140 \).

4. Repeat the process:

   • Determine how many times \( 16 \) fits into \( 140 \):
     • \( 16 \) goes into \( 140 \) eight times (since \( 16 \times 8 = 128 \)).
   • Subtract \( 128 \) from \( 140\):
     • \( 140 - 128 = 12 \).
   • Bring down another zero to make it \( 120 \).

5. Continue again:

   • Determine how many times \( 16 \) fits into \( 120 \):
     • \( 16 \) goes into \( 120 \) seven times (since \( 16 \times 7 = 112 \)).
   • Subtract \( 112 \) from \( 120\):
     • \( 120 - 112 = 8 \).
   • Bring down another zero to make it \( 80 \).

6. And continue once more:

   • Determine how many times \( 16 \) fits into \( 80 \):
     • \( 16 \) goes into \( 80 \) five times (since \( 16 \times 5 = 80 \)).
   • Subtract \( 80 \) from \( 80\):
     • \( 80 - 80 = 0 \).

So, putting all this together, we find: \[ 5 \frac{3}{16} = 5 + 0.1875 = 5.1875 \]

Thus, the correct answer is:

5.1875