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Not interested in getting valuable practice questions and articles delivered to your email? Obviously some numbers have more that one factor of 5. Now the base 5 problem We will employ a technique similar to that we used in base 10, but first lets make sure we know what we mean by base five.
Base five is a counting system where rather than there being 10 available digits 0 - 9 there are 5 0 - 4 hence the digits of a base 5 number represent from the right, 1's, 5's, 25's, 's etc. So the first few numbers in base 5 are 1, 2, 3, 4, 10, 11, 12, 13, 14, 20, Again we have to look at the sources of the zeros, only this time it's much easier.
Since 5 is a prime number then there is no way of making a zero other than by multiplying by a number that ends in a zero when written in base 5. You could write down all the numbers and count the zeros. See the table below. Number Base 10 Number Base 5 Zeros Number Base 10 Number Base 5 Zeros 2 95 1 90 1 85 1 80 1 75 2 70 1 65 1 60 1 55 1 50 2 45 1 40 1 35 1 30 1 25 2 20 40 1 15 30 1 10 20 1 5 10 1 Total 12 Total 12 Now in Binary The approach here is going to be roughly the same We need to think what would cause a zero to be on the end of the product of multiplication.
Significant figures of a number are digits which contribute to the precision of that number. Numbers that do not contribute any precision and should not be counted as a significant number are:.
The significance of trailing zeros in a number not containing a decimal point can be ambiguous. For example, it may not always be clear if a number like is precise to the nearest unit and just happens coincidentally to be an exact multiple of a hundred or if it is only shown to the nearest hundred due to rounding or uncertainty. Various conventions exist to address this issue:. When converting from decimal form to scientific notation, always maintain the same number of significant figures.
For example, 0. When multiplying and dividing numbers, the number of significant figures used is determined by the original number with the smallest amount of significant figures. When adding and subtracting, the final number should be rounded to the decimal point of the least precise number. It can be challenging to remember all the rules about significant figures and whether each zero is significant or not significant.
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