Rounded to three decimal places, $1.002^4 =$

Correct answer marked below

1.004

1.006

1.008

Correct

1.012

1.016

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Explanation

Preview

Official Explanation

Official

Using binomial expansion:

(1+\frac{1}{500})^4 = 1 + 4C1(1)^3(\frac{1}{500}) + 4C2(1)^2(\frac{1}{500})^2 + 4C3(1)(\frac{1}{500})^3 + 4C4(\frac{1}{500})^4

6*(\frac{1}{500})^2 = 0.000024

(Note: corrected calculation)

This is very small, so we can neglect the third, fourth, and fifth terms of the expansion.

Thus,

1.002^4 = 1 + \frac{4}{500} = 1.008

…

Comments

Be the first to share your thoughts and help others understand it better.

What this question tests

Your ability to convert between fractions, ratios, and decimals and to reason proportionally.

Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.