Math  /  Numbers & Operations

Question1) 207=\frac{20}{7}=

Studdy Solution

STEP 1

1. We need to convert the fraction 207\frac{20}{7} into a decimal.
2. The division will result in a repeating or terminating decimal.

STEP 2

1. Perform the division.
2. Interpret the result.

STEP 3

Perform the division of 2020 by 77.
Divide 2020 by 77 using long division:
1. 77 goes into 2020 a total of 22 times because 7×2=147 \times 2 = 14.
2. Subtract 1414 from 2020 to get a remainder of 66.
3. Bring down a zero to make the remainder 6060.
4. 77 goes into 6060 a total of 88 times because 7×8=567 \times 8 = 56.
5. Subtract 5656 from 6060 to get a remainder of 44.
6. Bring down another zero to make the remainder 4040.
7. 77 goes into 4040 a total of 55 times because 7×5=357 \times 5 = 35.
8. Subtract 3535 from 4040 to get a remainder of 55.
9. Bring down another zero to make the remainder 5050.
10. 77 goes into 5050 a total of 77 times because 7×7=497 \times 7 = 49.
11. Subtract 4949 from 5050 to get a remainder of 11.
12. Bring down another zero to make the remainder 1010.
13. 77 goes into 1010 a total of 11 time because 7×1=77 \times 1 = 7.
14. Subtract 77 from 1010 to get a remainder of 33.
15. Bring down another zero to make the remainder 3030.
16. 77 goes into 3030 a total of 44 times because 7×4=287 \times 4 = 28.
17. Subtract 2828 from 3030 to get a remainder of 22.
18. Bring down another zero to make the remainder 2020.

Notice that the remainder is back to 2020, which means the decimal will repeat from here.

STEP 4

Interpret the result.
The decimal representation of 207\frac{20}{7} is 2.8571422.857142 with the sequence 857142857142 repeating.
Thus, 207=2.857142\frac{20}{7} = 2.\overline{857142}.
The decimal representation of 207\frac{20}{7} is:
2.857142\boxed{2.\overline{857142}}

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