BigQuery - "random" number within a specified percentage of a number

rand_within_p.sql

-- implementation
WITH input AS (
  SELECT *
  FROM UNNEST([100,100,100,100,100,100,100,100,100,100]) x
  JOIN UNNEST([.4,.4,.4,.4,.4,.4,.4,.4,.4,.4]) p
)
SELECT x * (1 + (-p + (RAND() * (2 * p)))) AS rand_within_p_percent_of_x
FROM input;

-- verification of concept
WITH input AS (
  SELECT *
  FROM UNNEST([100,100,100,100,100,100,100,100,100,100]) x
  JOIN UNNEST([.4,.4,.4,.4,.4,.4,.4,.4,.4,.4]) p
),
calcs AS (
  SELECT x * (1 + (-p + (RAND() * (2 * p)))) AS rand_within_p_percent_of_x
  FROM input
)
SELECT min(rand_within_p_percent_of_x) AS min, max(rand_within_p_percent_of_x) AS max
FROM calcs

I'm aware that p is not a percentage, but I dislike multiplying things by 100 just to divide them by 100 later.