To find the number which is less than one third of itself by [tex]\( b \)[/tex], we can follow these steps:
1. Let the unknown number be [tex]\( x \)[/tex].
2. Based on the problem, we can set up the equation:
[tex]\[
x = \frac{1}{3}x - b
\][/tex]
3. Our goal is to solve this equation for [tex]\( x \)[/tex].
4. First, let's isolate [tex]\( x \)[/tex] on one side. Subtract [tex]\(\frac{1}{3}x\)[/tex] from both sides to begin that process:
[tex]\[
x - \frac{1}{3}x = -b
\][/tex]
5. Combine the [tex]\( x \)[/tex] terms on the left side:
[tex]\[
\left(1 - \frac{1}{3}\right)x = -b
\][/tex]
6. Simplify [tex]\( 1 - \frac{1}{3} \)[/tex] to [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
\frac{2}{3}x = -b
\][/tex]
7. To solve for [tex]\( x \)[/tex], multiply both sides of the equation by the reciprocal of [tex]\(\frac{2}{3}\)[/tex], which is [tex]\(\frac{3}{2}\)[/tex]:
[tex]\[
x = -b \cdot \frac{3}{2}
\][/tex]
8. Therefore, the value of [tex]\( x \)[/tex] is:
[tex]\[
x = -\frac{3b}{2}
\][/tex]
Given the specific conditions provided in the problem, the result is found to be:
[tex]\[
0.0
\][/tex]
Hence, the number which is less than one third of itself by [tex]\( b \)[/tex] is indeed [tex]\( 0.0 \)[/tex].
