And decrease by one, it is first zero, which shall be counted. To get first non zero element after comma, I've used such construction ("%.100f" % i).replace('.', '').index(k), where k run over interval. And last case, when i Little branching: i > 1.0 and i > 0.1 it is 10 and 1 respectively. So, first part, for input i > 1.0 - it is ten 10 in power of this length. This code based on principle of ten's power in len(str(int(float_number))).įloat number - converted to int, thereafter string str() from it, will give us a string with length which is we are looking exactly. This finds lots of failures in the naive implementation, but none in the improved implementation. Something along the lines of def nextpow10(n): So for a robust solution for floats and ints we need to assume that the value of our logarithm is only approximate, and we must therefore test a couple of possibilities. It is also theoretically possible for it to fail in the other direction, though this seems to be much harder to provoke. First of all n is converted from whatever data type it happens to have into a double precision floating point number, potentially introducing rounding errors, then the logarithm is calculated potentially introducing more rounding errors both in its internal calculations and in its result.Īs such it did not take me long to find an example where it gave an incorrect result. Unfortunately this suffers from rounding errors. In another answer it was proposed to take the logarithm, then round up (ceiling function), then exponentiate. Can your input values be any possible value of the types in question? or are they more constrained.If the input is exactly a power of 10 (or the closest floating point approximation of a power of 10), should the output be the same as the input? Or should it be the next power of 10 up? "10 -> 10" or "10 -> 100"? Let's assume the former for now.For results less than 1, what exactly do you want to round to? Do you want actual powers of 10 or floating point approximations of powers of 10? You are aware that negative powers of 10 can't be expressed exactly in floating point right? Let's assume for now that you want floating point approximations of powers of 10.What type(s) do you want for your outputs?.For example, in the exponential expression 10 2, the base 10 is used as a factor 2 times to represent 10 × 10 = 100.Your problem is under-specified, you need to step back and ask some questions. Same as a power.Ī way to write large numbers written using ten to a power, or exponent.Ī number system in which each number is 10 times the value to the right of it.Īny one of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 in the base-ten number system.Ī number written in the standard format, such as 100.Ī number written as a word, such as one hundred.Ī number written as repeated multiplication, such as 10 × 10.Ī way to write repeated multiplication using a base and exponent. For example, in 10 3 the base is 10, the exponent is 3, and 10 3 = 10 x 10 x 10 = 1,000. The numerical value that a digit has based on its position in a number.Ī small raised number used in exponential notation to tell how many times the base is used as a factor. The digits all move one place to the right. What is 10 × 10 × 10 × 10 written in exponential form? ANSWERĮxplain what happens to the digits in the number 765.4 when you find the quotient The digits move the number of spaces equal to the whole number exponent. How does the exponent tell you how digits move when you multiply or divide by a power of 10? ANSWER The digits shift to the right because the number gets smaller. When you divide a number by a power of 10, do the digits in the number shift right or left? Explain. The digits shift to the left because the number gets bigger. After Video When you multiply a number by a power of 10, do the digits in the number shift right or left? Explain.On a place-value chart, what place value is two places to the left of the thousands place? ANSWER On a place-value chart, what place is 1/100 of the thousands place? ANSWER What is the value of the 5 in 25,230? ANSWER Before Video What is the value of the 5 in the number 2,523? ANSWER.
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