You need to arrange three 7 and mathematical symbols to form number 1?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

'S' refers to the number of seconds in a day and 'H' refers to the number of hours in ten years. Which quantity out of these two is greater?

How many pluses should we put between the digits of 987654321 to get a total of 99, and where?

There are two candles. Both will only burn exactly for an hour. How will you use these two candles to measure forty-five minutes?

If 21x = 79x, what is the value of x?

Divide 110 into two parts so that one will be 150 per cent of the other. What are the 2 numbers?

If nine thousand, nine hundred nine dollars is written as $9,909,
how should twelve thousand, twelve hundred twelve dollars be written?

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.