Which of the following rational numbers can be expressed as a repeating decimal: 78, 512, 1725, or 3140?(1 point)

Answer 1

A rational number can be expressed as a repeating decimal if and only if its denominator contains prime factors other than 2 and 5.

Looking at the given numbers:

78 = (2)(3)(13) contains prime factors other than 2 and 5, so it can be expressed as a repeating decimal.
512 = (2^9) contains only prime factors of 2, so it cannot be expressed as a repeating decimal.
1725 = (3)(5^2)(23) contains prime factors other than 2 and 5, so it can be expressed as a repeating decimal.
3140 = (2^2)(5)(157) contains prime factors other than 2 and 5, so it can be expressed as a repeating decimal.

Therefore, the rational numbers that can be expressed as repeating decimals are 78, 1725, and 3140.

Answer 2

Express 713 as a repeating decimal. Mark the repeating digits with a bar.

Note: You will find the option to add a bar above text in the Geometry (∠
) keyboard.

(1 point)

Answer 3

To express 713 as a repeating decimal, we can divide 713 by a power of 10 so that the decimal part becomes a repeating decimal.

Let's divide 713 by 10:

71
______
10 | 713
-70
___
13

Next, we divide 713 by 100:

7.13
________
100 | 713
-700
_____
13

Finally, we divide 713 by 1000:

0.713
_________
1000 | 713
-7000
______
130
-1000
______
300
- 300
______
0

The decimal part does not repeat, so 713 cannot be expressed as a repeating decimal.

Answer 4

wrong

Answer 5

Apologies for the mistake. Let's try to express 713 as a repeating decimal correctly.

To express 713 as a repeating decimal, we can divide 713 by 99 (a two-digit number with both digits being 9). The reason for dividing by 99 is that when dividing a number by 99, the decimal part will repeat.

Let's perform the division:

7.212121...
_________________
99 | 713.000000...
-693
_________________
20

The remainder is 20, and since it is not zero, we can continue the division.

Now, we bring down another zero:

7.212121...
_________________
99 | 713.020000...
-693
_________________
200
- 198
________________
20

The remainder is again 20, and since it is the same as the previous remainder, the pattern will repeat indefinitely.

Therefore, the repeating decimal form of 713 is 7.212121..., with the digits 21 repeating.