Use long division to convert 3/16 to a decimal
To convert 3/16 to a decimal using long division, we divide the numerator (3) by the denominator (16) repeatedly until we either obtain a remainder of 0 or we have enough decimal places.
0.1875
-------------
16 | 3.0000
- 32
-----
1 (remainder)
We start by dividing the first digit of the numerator, 3, by the denominator, 16. The quotient is 0 (since 3 is less than 16), and we write it above the long division bar. Multiply this quotient by the denominator (16) and subtract the result from the numerator (3). This gives us a new remainder of 32.
Next, we bring down the next digit of the numerator (0) and add it to the remainder (32). We then divide this new number, 32, by the denominator, 16. The quotient is 2, which we write above the long division bar. Multiply this quotient by the denominator (16) and subtract the result from the remainder (32). This gives us a new remainder of 0.
Since the remainder is 0, we can stop the division. The quotient (above the division bar) is 0.1875. Therefore, 3/16 is equal to 0.1875 as a decimal.
Use long division to convert 11/20 to a decimal
To convert 11/20 to a decimal using long division, we divide the numerator (11) by the denominator (20) repeatedly until we either obtain a remainder of 0 or we have enough decimal places.
0.55
-------------
20 | 11.00
- 10
-----
10
- 10
-----
0
We start by dividing the first two digits of the numerator, 11, by the denominator, 20. The quotient is 0 (since 11 is less than 20), and we write it above the long division bar. Multiply this quotient by the denominator (20) and subtract the result from the numerator (11). This gives us a new remainder of 10.
Next, we bring down the next digit of the numerator (0) and add it to the remainder (10). We then divide this new number, 10, by the denominator, 20. The quotient is 0, which we write above the long division bar. Multiply this quotient by the denominator (20) and subtract the result from the remainder (10). This gives us a new remainder of 10.
We repeat the process and bring down the next digit of the numerator (0) and add it to the remainder (10). We divide this new number, 10, by the denominator, 20. The quotient is 0, which we write above the long division bar. Multiply this quotient by the denominator (20) and subtract the result from the remainder (10). This gives us a new remainder of 0.
Since the remainder is 0, we can stop the division. The quotient (above the division bar) is 0.55. Therefore, 11/20 is equal to 0.55 as a decimal.
Use long division to convert 3 4/5 to a decimal
To convert 3 4/5 to a decimal using long division, we first convert the mixed number to an improper fraction.
3 4/5 can be written as (3 * 5 + 4)/5 = 19/5.
Now we can proceed with long division:
3.8
---------
5 | 19.00
15
------
40
- 40
-------
0
We start by dividing the first two digits of the numerator, 19, by the denominator, 5. The quotient is 3, and we write it above the division bar. Multiply this quotient by the denominator (5) and subtract the result from the numerator (19). This gives us a new remainder of 4.
Next, we bring down the next digit of the numerator (0) and add it to the remainder (4). We then divide this new number, 40, by the denominator, 5. The quotient is 8, which we write above the division bar. Multiply this quotient by the denominator (5) and subtract the result from the remainder (40). This gives us a new remainder of 0.
Since the remainder is 0, we can stop the division. The quotient (above the division bar) is 3.8. Therefore, 3 4/5 is equal to 3.8 as a decimal.
Use long division to convert 13/20 to a decimal
To convert 13/20 to a decimal using long division, we divide the numerator (13) by the denominator (20) repeatedly until we either obtain a remainder of 0 or we have enough decimal places.
0.65
-------------
20 | 13.00
- 0
-----
130
- 120
-----
100
- 100
-----
0
We start by dividing the first two digits of the numerator, 13, by the denominator, 20. The quotient is 0 (since 13 is less than 20), and we write it above the long division bar. Multiply this quotient by the denominator (20) and subtract the result from the numerator (13). This gives us a new remainder of 13.
Next, we bring down a zero and add it to the remainder (13) to make 130. We then divide this new number, 130, by the denominator, 20. The quotient is 6, which we write above the division bar. Multiply this quotient by the denominator (20) and subtract the result from the remainder (130). This gives us a new remainder of 10.
We repeat the process and bring down another zero and add it to the remainder (10) to make 100. We divide this new number, 100, by the denominator, 20. The quotient is 5, which we write above the division bar. Multiply this quotient by the denominator (20) and subtract the result from the remainder (100). This gives us a new remainder of 0.
Since the remainder is 0, we can stop the division. The quotient (above the division bar) is 0.65. Therefore, 13/20 is equal to 0.65 as a decimal.
Use long division to convert 2/9 to a decimal. Your approximation should have one decimal place.
To convert 2/9 to a decimal using long division, we divide the numerator (2) by the denominator (9) repeatedly until we either obtain a remainder of 0 or we have enough decimal places.
0.2
-----------
9 | 2.00
- 18
-----
20
- 18
-----
20
- 18
-----
20
We start by dividing the first digit of the numerator, 2, by the denominator, 9. The quotient is 0 (since 2 is less than 9), and we write it above the long division bar. Multiply this quotient by the denominator (9) and subtract the result from the numerator (2). This gives us a new remainder of 2.
Next, we bring down a zero and add it to the remainder (2) to make 20. We then divide this new number, 20, by the denominator, 9. The quotient is 2, which we write above the division bar. Multiply this quotient by the denominator (9) and subtract the result from the remainder (20). This gives us a new remainder of 2.
We repeat the process and bring down another zero and add it to the remainder (2) to make 20. We divide this new number, 20, by the denominator, 9. The quotient is 2, which we write above the division bar. Multiply this quotient by the denominator (9) and subtract the result from the remainder (20). This gives us a new remainder of 2.
Since the remainder repeats as 2, we can assume that the decimal representation of 2/9 terminates and does not repeat. Therefore, 2/9 is approximately equal to 0.2 as a decimal with one decimal place.
Use long division to convert 27/50 to a decimal.(1 point)
To convert 27/50 to a decimal using long division, we divide the numerator (27) by the denominator (50) repeatedly until we either obtain a remainder of 0 or we have enough decimal places.
0.54
---------------
50 | 27.00
- 0
-----
270
- 250
-------
20
We start by dividing the first two digits of the numerator, 27, by the denominator, 50. The quotient is 0 (since 27 is less than 50), and we write it above the long division bar. Multiply this quotient by the denominator (50) and subtract the result from the numerator (27). This gives us a new remainder of 27.
Next, we bring down a zero and add it to the remainder (27) to make 270. We then divide this new number, 270, by the denominator, 50. The quotient is 5, which we write above the division bar. Multiply this quotient by the denominator (50) and subtract the result from the remainder (270). This gives us a new remainder of 20.
We repeat the process and bring down another zero and add it to the remainder (20) to make 200. We divide this new number, 200, by the denominator, 50. The quotient is 4, which we write above the division bar. Multiply this quotient by the denominator (50) and subtract the result from the remainder (200). This gives us a new remainder of 0.
Since the remainder is 0, we can stop the division. The quotient (above the division bar) is 0.54. Therefore, 27/50 is equal to 0.54 as a decimal.
Use long division to convert 3 3/8 to a decimal.(1 point)
To convert 3 3/8 to a decimal using long division, we first convert the mixed number to an improper fraction.
3 3/8 can be written as (3 * 8 + 3)/8 = 27/8.
Now we can proceed with long division:
3.375
---------
8 | 27.0000
- 24
-------
30
- 24
-------
60
- 56
-------
40
- 40
-------
0
We start by dividing the first digit of the numerator, 27, by the denominator, 8. The quotient is 3, and we write it above the division bar. Multiply this quotient by the denominator (8) and subtract the result from the numerator (27). This gives us a new remainder of 24.
Next, we bring down the next digit of the numerator (0) and add it to the remainder (24). We then divide this new number, 240, by the denominator, 8. The quotient is 30, which we write above the division bar. Multiply this quotient by the denominator (8) and subtract the result from the remainder (240). This gives us a new remainder of 56.
We repeat the process and bring down the next digit of the numerator (0) and add it to the remainder (56). We divide this new number, 560, by the denominator, 8. The quotient is 70, which we write above the division bar. Multiply this quotient by the denominator (8) and subtract the result from the remainder (560). This gives us a new remainder of 40.
Finally, we bring down the last digit of the numerator (0) and add it to the remainder (40). We divide this new number, 400, by the denominator, 8. The quotient is 50, which we write above the division bar. Multiply this quotient by the denominator (8) and subtract the result from the remainder (400). This gives us a new remainder of 0.
Since the remainder is now 0, we can stop the division. The quotient (above the division bar) is 3.375. Therefore, 3 3/8 is equal to 3.375 as a decimal.
Use long division to convert 4/15 to a decimal
To convert 4/15 to a decimal using long division, we divide the numerator (4) by the denominator (15) repeatedly until we either obtain a remainder of 0 or we have enough decimal places.
0.2666...
---------------
15 | 4.00000
- 30
------
10
- 0
------
We start by dividing the first digit of the numerator, 4, by the denominator, 15. The quotient is 0 (since 4 is less than 15), and we write it above the long division bar. Multiply this quotient by the denominator (15) and subtract the result from the numerator (4). This gives us a new remainder of 4.
Next, we bring down a zero and add it to the remainder (4) to make 40. We then divide this new number, 40, by the denominator, 15. The quotient is 2, which we write above the division bar. Multiply this quotient by the denominator (15) and subtract the result from the remainder (40). This gives us a new remainder of 10.
Since the remainder is now 10, we bring down another zero and add it to the remainder (10) to make 100. We divide this new number, 100, by the denominator, 15. The quotient is 6, which we write above the division bar. Multiply this quotient by the denominator (15) and subtract the result from the remainder (100). This gives us a new remainder of 10.
Since the remainder keeps repeating as 10, we can assume that the decimal representation of 4/15 repeats the digit 6 after the decimal point. Therefore, 4/15 is approximately equal to 0.26 (or 0.2666...) as a decimal.
wrong the choices are 4.15 0.27 3.75 or 26
My apologies for the incorrect explanation earlier. Let's use long division to convert 4/15 to a decimal again:
0.2666...
---------------
15 | 4.00000
- 30
------
10
- 0
------
We start by dividing the first digit of the numerator, 4, by the denominator, 15. The quotient is 0 (since 4 is less than 15), and we write it above the long division bar. Multiply this quotient by the denominator (15) and subtract the result from the numerator (4). This gives us a new remainder of 4.
Next, we bring down a zero and add it to the remainder (4) to make 40. We then divide this new number, 40, by the denominator, 15. The quotient is 2, which we write above the division bar. Multiply this quotient by the denominator (15) and subtract the result from the remainder (40). This gives us a new remainder of 10.
Since the remainder is now 10, we bring down another zero and add it to the remainder (10) to make 100. We divide this new number, 100, by the denominator, 15. The quotient is 6, which we write above the division bar. Multiply this quotient by the denominator (15) and subtract the result from the remainder (100). This gives us a new remainder of 10.
Since the remainder repeats as 10, we know that the decimal representation of 4/15 doesn't terminate but repeats the digit 2 after the decimal point. Therefore, 4/15 is equal to 0.2 as a decimal.
Out of the given choices, the closest approximation is 0.27.
Use long division to convert 711 to a decimal.(1 point)
Responses
≈1.571428
approximately equals 1.571428
≈0.63
approximately equals 0.63
63
63
7.11
To convert 711 to a decimal using long division, we divide 711 by 1. Here's how the long division would look:
711.0000
---------
1 | 711.0000
- 711
-----
0
We divide 711 by 1, which gives us a quotient of 711 and a remainder of 0. Therefore, 711 is equal to 711.0 as a decimal. However, since there is no decimal part or recurring pattern in the remainder, we don't need to include any decimal places. Therefore, the correct response is 711.
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
63
63
7.11
To convert 7/11 to a decimal using long division, we divide the numerator (7) by the denominator (11) repeatedly until we either obtain a remainder of 0 or we have enough decimal places.
0.636363...
---------------
11 | 7.00000
- 66
------
40
- 33
------
70
- 66
------
40
We start by dividing the first digit of the numerator, 7, by the denominator, 11. The quotient is 0 (since 7 is less than 11), and we write it above the long division bar. Multiply this quotient by the denominator (11) and subtract the result from the numerator (7). This gives us a new remainder of 7.
Next, we bring down a zero and add it to the remainder (7) to make 70. We then divide this new number, 70, by the denominator, 11. The quotient is 6, which we write above the division bar. Multiply this quotient by the denominator (11) and subtract the result from the remainder (70). This gives us a new remainder of 40.
We repeat the process and bring down another zero and add it to the remainder (40) to make 400. We divide this new number, 400, by the denominator, 11. The quotient is 36, which we write above the division bar. Multiply this quotient by the denominator (11) and subtract the result from the remainder (400). This gives us a new remainder of 40.
Since the remainder repeats as