How to use bigquery round up results to 4 digits after decimal point?

Depends on your coding preferences - for example you can just use simple ROUND(floatvalue, 4)
Depends on how exactly you need to round - up or down - you can respectively adjust expression
For example ROUND(floatvalue + 0.00005, 4)

See all rounding functions for BigQuery Standard SQL at below link

https://cloud.google.com/bigquery/docs/reference/standard-sql/functions-and-operators#rounding-functions

Note that this question deserves a different answer now.

The premise of the question is "We don't have decimal data type in BigQuery now."

But now we do: You can use NUMERIC:

SELECT CAST('0.029' AS NUMERIC)*50/100

# 0.0145

Just make your column is NUMERIC instead of FLOAT64, and you'll get the desired results.