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Q: A certain two-digit number is equal to 9 times the sum of its digitIf 63 were subtracted from the number the digits would be reversed Find the number?

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write down the first three digits.look at the fourth digitif it is 5 or more, add one to what you have written down so far (ie round up)replace all digits from the fourth onwards by zeros.if any zero after the third digit is after a decimal point, rub them out.That's HOW to do it, this is it being done:3951.675 to 3 sig fig is 3950

The easiest way is to convert the mixed numbers and fractions to decimals by dividing the numerators (top) numbers by the denominator (bottom) numbers of each fraction - for a mixed number, the whole number needs to be added on.Then, comparing the whole numbers order as much as possible the numbers. Start with the tenths digit (the digit immediately to the right of the decimal point)Sort those groups of numbers with the same digits so far based on the current decimal digitIf there are still groups of numbers, use the next decimal digit (hundredth, thousandth, etc) until a distinction can be made.Where there are a group of numbers with the same whole number, start looking at the decimal digits:Write the list out of numbers out in their original form (decimal, fraction or mixed number).

If you mean a straight forward algorithm, then yes.I guess you want to know what it is...Start at the left hand end of the binary number with the result (decimal number) set to zerodouble the result and add the current binary digitif there are more binary digits move one binary digit to the right and repeat step 2repeat steps 2 and 3 until all the binary digits have been used.the result is the decimal equivalentfor example converting 101002 to decimal:1. set result to 0, start with the first binary digit (of 10100) which is 12. 2 x 0 + 1 = 13. 2nd binary digit (of 10100) is 02. 2 x 1 + 0 = 23. 3rd binary digit (of 10100) is 12. 2 x 2 + 1 = 53. 4th binary digit (of 10100) is 02. 2 x 5 + 0 = 103. 5th binary digit (of 10100) is 02. 2 x 10 + 0 = 203. no more binary digits4. 101002 = 2010

You have given no base for the 1110, so you'll have to do the conversion yourself by writing the place column values over the digits:write 1 over the rightmost digit.start with the digit to the left of the rightmost digit:write the value over the digit to the right of the current digit multiplied by the base over the digitmove left one digitif you have not run out of digits repeat from step 3.Now that you have written the place column values, the number 1110 (in whatever base it is) can be converted to base 10 by summing all the digits of the number multiplied by the place column value over it. eg if 1110 is in octal (base 8), this gives:512___64___8___1_1______1___1___0→ 1110 base 8 = 512 × 1 + 64 × 1 + 8 × 1 + 1 × 0 = 512 + 64 + 8 = 584 in base 10.If the 1110 is not in base 8, you'll have to do the conversion yourself.You may notice that the place column value are 8 to the power of the number of columns to the left of the ones column:512 = 8³64 = 8²8 = 8¹1 = 8⁰→ 512__64__8__1 place column values are 8³__8²__8¹__8⁰This is true of any base, eg base 10:10³__10²__10¹__10⁰ is equivalent to 1000__100__10__1so 1234 would be 1 × 1000 + 2 × 100 + 3 × 10 + 4 × 1.

The nth triangular number is given by ½ × n × (n+1)→ the 5857th triangular number is ½ × 5857 × 5858 = 17,155,153, so its units digit is a 3.------------------------------------------------------------Alternatively,If you look at the units digits of the first 20 triangular numbers they are {1, 3, 6, 0, 5, 1, 8, 6, 5, 5, 6, 8, 1, 5, 0, 6, 3, 1, 0, 0}At this stage, as we are only concerned with the units digit, as we now have a 0 for the units digit, when 21 is added it is the same as adding 1 to 0 to give a 1, for the 22nd triangular number, we are adding 2 to the 1 to give 3, and so on - the sequence of 20 digits is repeating.To find the units digit of the nth triangular number, find the remainder of n divided by 20 and its units digit will be that digit in the sequence (if the remainder is 0, use the 20th number). To find the remainder when divided by 20 is very simple by looking at only the tens digit and the units digit:If the tens digit is even (ie one of {0, 2, 4, 6, 8}), the remainder is the units digitIf the tens digit is odd (ie one of {1, 3, 5, 7, 9}), the remainder is the units digit + 10.5857 ÷ 20 = ... remainder 17; the 17th digit of the above sequence is a 3, so the units digit of the 5857th triangular number is a 3.This trick can be used for much larger triangular numbers which calculators cannot calculate exactly using the above formula. eg the units digit of the 1234567890123456789th triangular number is... 1234567890123456789 ÷ 20 = .... remainder 9, so this triangular number's units digit is the 9th digit of the above sequence which is a 5.

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