Many students are curious why 1.02³ does not equal 1.08 when working with factors and decimals. A small number raised to a tiny influence might seem to deliver an easily understood outcome. The right response, though, may surprise a lot of people. We must look into the theoretical basis behind variables and find a simple, clear solution to such problems in order to figure out why 1.02³ does not equal 1.08.
We’ll break down the idea in detail in the following paragraphs. We’ll go over why 1.02³ does not equal 1.08, how to figure it correctly, and a shortcut you can use to keep clear of similar problems.
Think before you write!
We should look at the essay’s main argument prior to getting into the figures themselves. Why does 1.02³ not equal 1.08 is the specific question we would like to the location. The goal is to assist readers in comprehending the source of the error and how to answer such questions more quickly and specifically.
After reading this piece, readers should to be able to:
- Know the method of exponential growth.
- Learn about why 1.02³ is not equivalent to 1.08.
- To find the right answer fast, use a shortcut
- Keep clear of usual mistakes in subsequent computations.
Begin to now talk about framework and justification.
What does 1.02³ actually mean?
We must first define 1.02³ before we can give an answer to the question, Why does 1.02³ not equal 1.08? 1.02³ is the same as 1.02 × 1.02 × 1.02 in mathematics.
Three times, we are multiplying 1.02 by itself. because 1.02 is only slightly higher than 1.00, many people believe that this should be near 1.08. However, the result is more than anticipated when it is multiplied three times.
Let us break it in detail.
Step-by-step calculation
take steps to calculate: 1.02 × 1.02 = 1.0404
1.0404 × 1.02 = 1.061208
Thus, 1.02³ produces 1.061208 versus 1.08. There is a noticeable difference. We can now see why the initial belief was wrong.
Why, then, is 1.02³ not equal to 1.08?
Because the result grows more slowly than most people anticipate when small decimal numbers are multiplied multiple times.
Why people think 1.02³ equals 1.08
Many people make predicts without doing any math and believe that 1.02 × 3 = 3.06 3.06 ÷ 3 = approximately 1.02.
Thus, 1.02³ ≈ 1.08
An exponentiation or adding a number to a power, is not the same as multiplying by that number, so this line of thinking is flawed.
1.02³ is not equivalent to 1.02 × 3. It is equivalent to 1.02 times itself. This is a major uniqueness. Because of this, a lot of adults and students make mistakes.
Why does 1.02³ not equal 1.08? The shortcut to finding the correct answer
Now that we know the right reply, let’s get started look into a quick fix for this type of problem that doesn’t require lengthy multiplication.
Shortcut: For humbleness goes up, apply the power formula.
This formula can be used if a number, like 1.02, is near to 1 and is raised to a small power, like 3.
(1 + r)ⁿ≈ 1 + nr + n(n − 1)r2 / 2
Here:
- For 1.02, r = 0.02, where a is the increase over 1.
- The exponent is n (n = 3).
Enter the following numbers now:
1 + 3(0.02) + 3(2)(0.02)² / 2 = 1 + 0.06 + 3(2)(0.0004)/2 = 1 + 0.06 + (3 × 2 × 0.0004) ÷ 2 = 1 + 0.06 + 0.0012 = 1.0612
That is nearly the exact response (1.061208). Therefore, for small numbers like this, the shortcut formula performs superbly.
Why does 1.02³ not equal 1.08? Finally, says
Going back to the primary query, why is 1.02³ not equal to 1.08?
Since 1.02³ = 1.061208 rather than 1.08, the answer is straightforward. This error occurs when we estimate rather than comprehend the true meaning of exponentiation.
The formula for (1 + r)ⁿ also taught us a handy shortcut that yields almost flawless results for small values of r and n. You can save time and stay clear of typical mistakes in math tests and everyday problem-solving by doing this.
You’ll know the right answer—and how to find it quickly—the next time someone asks, Why does 1.02³ not equal 1.08?