返回题库

HMMT 十一月 2014 · 冲刺赛 · 第 8 题

HMMT November 2014 — Guts Round — Problem 8

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 7 ] Find the number of digits in the decimal representation of 2 .
解析

英文解析

  1. [ 7 ] Find the number of digits in the decimal representation of 2 .
    Answer: 13 Noticing that 2 = 1024 ≈ 1000 allows for a good estimate. Alternatively, the 10
    number of decimal digits of n is given by ⌊ log ( n ) ⌋ + 1. Using log (2) ≈ 0 . 31 also gives the correct
    10 10
    answer. The exact value of 2 is 2199023255552.41