# MSC #30 – “By Inspection”

We reserved this Sutra for the last of our ** 30 MATH-Inic Specials for Christmas** because it depends largely on how much one has mastered the concepts presented in the previous specials. It also encourages adaptation and stimulates creativity because it shows how some problems can be easily solved

**or**

*By Inspection***.**

*By Mere Observation*As an example, we used **385 x 999**. The answer can be readily obtained by using two sutras, ** By one less than the one before **and

**.**

*All from 9 and the last from 10*The first part of the answer comes from **385 – 1 = 384**, while the second part is the **10’s** complement of **385: 1000 – 385 = 615**. So **385 x 999 = 384,615**.

Or after getting the first part **384**,
just get the **9’s** complement of **384**. In case there is a confusion
in what rule to follow, it is best to use use “the last by the last” the last
digits of the factors are **5** and **9** so the last digit of the
product must be **5**

Just by looking at the figures, we can announce the answer.

An interesting application of this is getting the recurring decimal equivalent of a fraction with a denominator of **13** like **5/13**, for instance.

- 5 x 7 = 35 (By Inspection)
- 35 x 11 = 385 (By Inspection)
- 385 x 999 = 384,615(By Inspection)
- 5/13 = 0. 384615…

Note that:

1/1001 = 0.000999

5/ (7 x 11 x 13) = (5 x 999)/1,000,000)

5/13 = (5 x 7 x 11 x 999)/1,000,000

More examples of solving “by Inspection” are discussed in Chapter 30 of “30 Master Strategies in Computing”