simplify (1+(0.01)/2)^2-1 — step-by-step solution

Let's reduce:

{(1 + \frac{0.01}{2})}^{2} - 1

ⅰ

\frac{0.01}{2}

0.005

{(1 + 0.005)}^{2} - 1

ⓘ Parentheses are computed first:

1 + 0.005

1.005

{1.005}^{2} - 1

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product:

{1.005}^{2}

1.005 \times 1.005

\approx 1.0100

\approx 1.0100 - 1

ⓘ Start from

\approx 1.0100

and move back

1

on the number line:

\approx 1.0100 - 1

1.0025 \times 10^{- 2}

▶Simplified form:

1.0025 \times 10^{- 2}