Math SAT Blue book question help

Test Preparation SAT Preparation
1

<p>How do you do this problem quickly?</p>

<p>5.10100100010000100000</p>

<p>The deciam number above consists of only 1's and 0's to the right of the decimal point. The first 1 is followed by one 0, the second 1 is followed by two 0's, the third 1 is followed by three 0's, and so on. What is the total number of 0's between the 98th and the 101st 1 in this decimal number?</p>

2

<p>You know how many zeros come after each 1 (n zeroes after the nth 1) </p>

<p>So after the 98th 1 is 98 zeros</p>

<p>Between 98th 1 and 101st 1 you have
98 zeros +
99 zeros +
100 zeros</p>

<p>don't count 101, because those zeros are after the 101st 1. </p>

<p>so it's 98+99+100 = 297</p>

3

<p>I think I get it...</p>