In the repeating decimal 0.934, what digit is in the 28th decimal place?
To find the digit in the 28th decimal place, we need to first convert 0.934 into a repeating decimal. 0.934 can be written as 0.933333... because the digit 3 repeats infinitely.
To determine the digit in the 28th decimal place, we need to find the remainder when 28 is divided by the number of repeating digits, which is 3.
28 ÷ 3 = 9 remainder 1
Therefore, the digit in the 28th decimal place is the same as the digit in the 1st decimal place, which is 3.
To find the digit in the 28th decimal place of the repeating decimal 0.934, we need to determine the period of the repeating part.
To convert the decimal 0.934 to a fraction, we first remove the decimal point and use the number of decimal places as the denominator. Since there are three decimal places, the fraction becomes 934/1000.
Simplifying this fraction by dividing both numerator and denominator by their common factor of 2, we get 467/500.
To find the period of the repeating part, we can convert the fraction 467/500 to a decimal using long division:
0.93400
____________
500 | 467.000
-500
-----
11.000
-10.00
-----
1.000
- 1.000
-----
0.000
As we can see from the long division, the division terminates, so the repeating part has a period of 0. Therefore, there is no digit in the 28th decimal place.