Difference between revisions of "1997 AJHSME Problems/Problem 6"

 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
The digit "9" is 6 places to the left of the digit "3". Thus, it has a place value that is <math>10^{6-1}</math> times greater.
+
==Problem==
 +
 
 +
In the number <math>74982.1035</math> the value of the ''place'' occupied by the digit 9 is how many times as great as the value of the ''place'' occupied by the digit 3?
 +
 
 +
<math>\text{(A)}\ 1,000 \qquad \text{(B)}\ 10,000 \qquad \text{(C)}\ 100,000 \qquad \text{(D)}\ 1,000,000 \qquad \text{(E)}\ 10,000,000</math>
 +
 
 +
==Solution 1==
 +
The digit <math>9</math> is <math>5</math> places to the left of the digit <math>3</math>. Thus, it has a place value that is <math>10^5 = 100,000</math> times greater.
 
<math>\boxed{\textbf{(C)}}</math>
 
<math>\boxed{\textbf{(C)}}</math>
 +
 +
==Solution 2==
 +
The digit <math>9</math> is in the <math>100</math>s place.  The digit <math>3</math> is in the <math>\frac{1}{1000}</math>ths place.  The ratio of these two numbers is <math>\frac{100}{\frac{1}{1000}} = 100\times1000 = 100,000</math>, and the answer is <math>\boxed{\textbf{(C)}}</math>
 +
 +
 +
== See also ==
 +
{{AJHSME box|year=1997|num-b=5|num-a=7}}
 +
* [[AJHSME]]
 +
* [[AJHSME Problems and Solutions]]
 +
* [[Mathematics competition resources]]
 +
{{MAA Notice}}

Latest revision as of 00:26, 5 July 2013

Problem

In the number $74982.1035$ the value of the place occupied by the digit 9 is how many times as great as the value of the place occupied by the digit 3?

$\text{(A)}\ 1,000 \qquad \text{(B)}\ 10,000 \qquad \text{(C)}\ 100,000 \qquad \text{(D)}\ 1,000,000 \qquad \text{(E)}\ 10,000,000$

Solution 1

The digit $9$ is $5$ places to the left of the digit $3$. Thus, it has a place value that is $10^5 = 100,000$ times greater. $\boxed{\textbf{(C)}}$

Solution 2

The digit $9$ is in the $100$s place. The digit $3$ is in the $\frac{1}{1000}$ths place. The ratio of these two numbers is $\frac{100}{\frac{1}{1000}} = 100\times1000 = 100,000$, and the answer is $\boxed{\textbf{(C)}}$


See also

1997 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png