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

Responses

5.4
5.4

0.54
0.54

1.851
1.851

27.5

11 answers

To convert \( \frac{27}{50} \) to a decimal using long division, follow these steps:

  1. Set up the division: 27 is the dividend and 50 is the divisor. Since 27 is less than 50, we will treat 27 as 27.00 (adding decimal places) for the purpose of division.

  2. Determine how many times 50 fits into 27: It fits 0 times. Put 0 before the decimal point.

  3. Bring down a zero: Now consider 270 (bringing down the first 0).

  4. Divide:

    • 50 goes into 270 five times (because \( 50 \times 5 = 250 \)).
    • Write 5 after the decimal point, so we have 0.5.

  5. Subtract:

    • \( 270 - 250 = 20 \).

  6. Bring down another zero: Now consider 200 (bringing down the next 0).

  7. Divide:

    • 50 goes into 200 four times (because \( 50 \times 4 = 200 \)).
    • Write 4 after the 5, so we have 0.54.

  8. Subtract:

    • \( 200 - 200 = 0 \).

Since there is no remainder, the division is complete.

Thus, the decimal representation of \( \frac{27}{50} \) is 0.54.

The correct response is: 0.54

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

3.375
3.375

33.75
33.75

0.375
0.375

2.66
2.66

To convert the mixed number \( 3 \frac{3}{8} \) to a decimal, we can break it down into its components. The whole number part is \( 3 \) and the fractional part is \( \frac{3}{8} \).

  1. Convert the fraction \( \frac{3}{8} \) to a decimal using long division:

    • Set up the division: 3 is the dividend and 8 is the divisor.
    • Since 3 is less than 8, we can consider it as \( 3.000 \) and perform the division.

    Long Division Steps:

    1. 8 goes into 3, 0 times. Write 0.
    2. Bring down the first 0 (making it 30).
    3. 8 goes into 30, 3 times (because \( 8 \times 3 = 24 \)).
    4. Subtract \( 30 - 24 = 6 \).
    5. Bring down the next 0 (making it 60).
    6. 8 goes into 60, 7 times (because \( 8 \times 7 = 56 \)).
    7. Subtract \( 60 - 56 = 4 \).
    8. Bring down the next 0 (making it 40).
    9. 8 goes into 40, 5 times (because \( 8 \times 5 = 40 \)).
    10. Subtract \( 40 - 40 = 0 \).

    Final result: So, \( \frac{3}{8} = 0.375 \).

  2. Combine the whole number and the decimal:

    • The whole number part is \( 3 \).
    • The decimal part we calculated is \( 0.375 \).

Therefore, \( 3 \frac{3}{8} = 3 + 0.375 = 3.375 \).

The correct response is: 3.375

Use long division to convert 4/15 to a decimal.(1 point)
Responses

26
26

4.15
4.15

≈0.27
approximately equals 0.27

3.75
3.75

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

  1. Set up the division: Write 4 as the dividend and 15 as the divisor. Since 4 is less than 15, we can treat it as \( 4.000 \) for the purpose of division.

  2. Determine how many times 15 fits into 4:

    • It fits 0 times. Write 0 before the decimal point.

  3. Bring down a zero: Now consider 40 (by bringing down the first 0).

  4. Divide:

    • 15 goes into 40 two times (because \( 15 \times 2 = 30 \)).
    • Write 2 after the decimal point, so we have 0.2.

  5. Subtract:

    • \( 40 - 30 = 10 \).

  6. Bring down another zero: Now consider 100 (by bringing down the next 0).

  7. Divide:

    • 15 goes into 100 six times (because \( 15 \times 6 = 90 \)).
    • Write 6, so now we have 0.26.

  8. Subtract:

    • \( 100 - 90 = 10 \).

  9. Bring down another zero: Now consider 100 again (by bringing down another 0).

  10. Divide once more:

    • 15 goes into 100 six times (again, \( 15 \times 6 = 90 \)).
    • Write another 6, so we have 0.266.

You can continue this process, but it’s clear that the decimal is repeating at this point, leading to \( 0.2666... \)

For practical purposes, we can round this and approximate it:

The approximate value of \( \frac{4}{15} \) is approximately 0.27.

The correct response is: ≈0.27

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

≈0.63
approximately equals 0.63

63
63

7.11
7.11

≈1.571428

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

  1. Set up the division: 7 is the dividend, and 11 is the divisor. Since 7 is less than 11, we can treat it as \( 7.000 \) (adding decimal places) for the purpose of division.

  2. Determine how many times 11 fits into 7:

    • It fits 0 times. Write 0 before the decimal point.

  3. Bring down a zero: Now consider 70 (bringing down the first 0).

  4. Divide:

    • 11 goes into 70 six times (because \( 11 \times 6 = 66 \)).
    • Write 6 after the decimal point, so we have 0.6.

  5. Subtract:

    • \( 70 - 66 = 4 \).

  6. Bring down another zero: Now consider 40 (bringing down the next 0).

  7. Divide:

    • 11 goes into 40 three times (because \( 11 \times 3 = 33 \)).
    • Write 3 after the 6, so we have 0.63.

  8. Subtract:

    • \( 40 - 33 = 7 \).

  9. Bring down another zero: Now consider 70 again (bringing down another 0).

  10. Divide again:

    • 11 goes into 70 six times (which we have already calculated).
    • Write another 6 after the 3, maintaining 0.636.

You begin to see that the numbers repeat. Thus, \( \frac{7}{11} = 0.636363...\), which is often written as \( 0.\overline{63} \).

For rounding, we can say that:

The approximate value of \( \frac{7}{11} \) is approximately 0.63.

The correct response is: ≈0.63

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

5.36
5.36

≈5.3
approximately equals 5.3

5.1875
5.1875

0.1875

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

  1. Convert the fraction \( \frac{3}{16} \) to a decimal using long division:

    • Set up the division: 3 is the dividend and 16 is the divisor. Since 3 is less than 16, we treat it as \( 3.000 \) for the division.

    Long Division Steps:

    1. 16 goes into 3, 0 times. Write \( 0 \).
    2. Bring down the first 0 (making it 30).
    3. 16 goes into 30, 1 time (because \( 16 \times 1 = 16 \)).
    4. Subtract \( 30 - 16 = 14 \).
    5. Bring down the next 0 (making it 140).
    6. 16 goes into 140, 8 times (because \( 16 \times 8 = 128 \)).
    7. Subtract \( 140 - 128 = 12 \).
    8. Bring down the next 0 (making it 120).
    9. 16 goes into 120, 7 times (because \( 16 \times 7 = 112 \)).
    10. Subtract \( 120 - 112 = 8 \).
    11. Bring down the next 0 (making it 80).
    12. 16 goes into 80, 5 times (because \( 16 \times 5 = 80 \)).
    13. Subtract \( 80 - 80 = 0 \).

    Final result: So, \( \frac{3}{16} = 0.1875 \).

  2. Combine the whole number with the decimal:

    • The whole number part is \( 5 \).
    • The decimal part we calculated is \( 0.1875 \).

Thus, \( 5 \frac{3}{16} = 5 + 0.1875 = 5.1875 \).

The correct response is: 5.1875

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