What number is to be subtracted from 0.006898 to make it a perfect square?

Answer: 0.000009

• Write 0.006898 as a fraction with denominator 1,000,000: 0.006898 = 6898/1,000,000.

• A decimal that is a perfect square with denominator 1,000,000 must have a numerator that is a perfect square. Find an integer k with k^2 ≤ 6898.

• Compute squares: 83^2 = 6889 and 84^2 = 7056, so the largest square not exceeding 6898 is 6889 = 83^2.

• Therefore the nearest smaller perfect-square decimal is 6889/1,000,000 = (83/1000)^2 = 0.006889.

• Subtract to find the required amount: 0.006898 − 0.006889 = 0.000009.

Thus the number to be subtracted is 0.000009.