Grades 9-10 Video Solutions 2013-Level 9&10 Video Solutions 2013 problem21

Level 9&10 Video Solutions 2013 problem21

Video Transcription

Video Summary

The problem involves determining how many digits are needed after the decimal point for the number \(1 \div 1,024,000\) to be expressed with the smallest possible number of digits. By factoring \(1,024,000\) as \(2^{10} \times 5^3\) and applying this to our expression, we establish the condition that the minimum number of digits \(n\) after the decimal will result when \(n - 3 = 10\), because the factors of 2 and 5 must be balanced to form an integer. This gives \(n = 13\), so there are 13 digits after the decimal point.

Keywords

decimal digits

division

factorization

integer expression

minimum digits