what is the biggest technological industry in the world?

Mobile phone related technology is the biggest tech industry in the world.

For example: Building mobile applications to use in a smart phone such as apple iphone, samsung phones, google phones etc.

refer below

https://money.usnews.com/investing/stock-market-news/slideshows/the-10-most-valuable-tech-companies-in-the-world?slide=11

Hey Sabina – love this question. There are several tech industries that are making a big impact in our world today. In the Business to business space, the software as a service (SaaS) industry is rapidly growing (Salesforce as a company is an example) and there is a lot of opportunity in this area for a lot of different types of jobs (engineering, marketing, finance, etc.). There are also other areas like Artificial Intelligence and Robots that are taking our world by force. More and more companies are creating businesses that focus on these things and there's a lot of opportunity for growth and jobs!