Best Answer

Let us look at this with an example. Say you want to find the second last digit of 5,283,641267.

The first step is to recognise that the 5,283,600 part of the mantissa will contribute nothing to the last two digits. So you can ignore them completely. That simplifies the question to finding the second last digit of 41267.

The hard work starts now. You examine the last two digits of the powers of 41 to see if there is a pattern.

1) 41*1 = 41

2) 41*41 = 1681 => 81

3) 81*41 = 3321 => 21

4) 21*41 = 861 => 61

5) 61*41 = 2501 => 01

6) 01*41 = 41

The last two digits of 411are the same as the last two digits of 416. The difference in exponents is 5 and that is the key number for this example. What that says is that every 5th power you return to where you started. As a result, you can reduce the exponent by 5 (or multiples of 5) without changing the last two digits.

The exponent in the question is 267. Find the remainder when 267 is divided by 5. The remainder is 2 and so the last two digits are the same as those of 412, that is, 81. And so the second last digit is 8.

Warnings:

- Some numbers do not return to their starting point (odd multiples of 2 or 5: for example, 02). But 22and 222both end in 04. The difference in exponents is 20 and so you can reduce the exponent by multiples of 20. Except that, if at the end of these reductions, the remainder is 1, you need to look at 221and not 21.
- Many numbers have a cycle of length 20, so be patient.

Q: How do you find out the second last digit of a large exponent?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

In such cases, you should compare one digit at a time, from left to right, until you find a digit that is different in the two numbers. That is, compare the first digit (after the decimal period) with the first digit, the second digit with the second digit, etc.

Look for the first digit that is different. In this case, the first digit after the decimal point. The number that has the larger digit in this position, is larger. If the first digit is the same, compare the second digit with the second digit, the third digit with the third digit, and so forth, until you find a difference.

Since there is no whole part, compare the digits after the decimal point one by one (first digit with first digit, second digit with second digit, etc.), until you find two digits that are different.

Cut the exponent in half.

Find the reciprocal of the positive exponent. Thus, x-a = 1/xa

Related questions

In such cases, you should compare one digit at a time, from left to right, until you find a digit that is different in the two numbers. That is, compare the first digit (after the decimal period) with the first digit, the second digit with the second digit, etc.

Look for the first digit that is different. In this case, the first digit after the decimal point. The number that has the larger digit in this position, is larger. If the first digit is the same, compare the second digit with the second digit, the third digit with the third digit, and so forth, until you find a difference.

Ans: 462

Just compare the digits one by one: compare the first digit after the decimal point with the first digit of the other number, the second digit with the second digit, etc., until you find a digit that is different.

Since the whole part is the same, compare each of the decimal digits (compare the first digit with the first digit, the second digit with the second digit, etc.), until you find a pair that is different.

Since there is no whole part, compare the digits after the decimal point one by one (first digit with first digit, second digit with second digit, etc.), until you find two digits that are different.

One can easily find the units digit by looking for a pattern. For numbers with large powers, they will have a pattern that keeps repeating like a cycle. Depending on the multiple of the power, the pattern can be compared to find the units digit.

Cut the exponent in half.

To compare the two numbers, compare the first digit after the decimal point, then the second, etc., until you find a digit that is different.

Since the integer part is the same, you need to compare the decimal digits, one at a time.That is, compare the first digit with the first digit; if (as in this case) they are the same, you compare the second digit with the second digit - until you find two digits that are different in the same position.

Find the reciprocal of the positive exponent. Thus, x-a = 1/xa

The same way as you find the square root with an even-numbered exponent. For example, the square root of x10 is x5. That is, divide the exponent by 2. Similarly, the square root of x7 is x3.5. Once again, you simply calculate one-half of the exponent. If you prefer to express this with integer exponents and square roots, in this example you can write x3.5 as x3x0.5. The second part, x0.5, is equivalent to the square root of "x".