What is 12% of 4% of 7% of 2 × 10 6 ?
672
Calculating Percentage of Percentage
The question asks us to find a series of percentages of a given number. We need to calculate 12% of 4% of 7% of $2 \times 10^6$. This means we will perform the calculations step by step, working from the innermost percentage outwards.
The number is $2 \times 10^6$, which is equal to $2 \times 1,000,000 = 2,000,000$.
Step-by-Step Percentage Calculation
Let's break down the calculation into stages:
Stage 1: Calculate 7% of $2 \times 10^6$
To find 7% of $2 \times 10^6$, we multiply $2 \times 10^6$ by the decimal equivalent of 7%, which is 0.07, or by the fraction $\frac{7}{100}$.
So, 7% of $2 \times 10^6$ is 140,000.
Stage 2: Calculate 4% of the result from Stage 1
Next, we need to find 4% of 140,000. We multiply 140,000 by the decimal equivalent of 4%, which is 0.04, or by the fraction $\frac{4}{100}$.
So, 4% of 140,000 is 5,600.
Stage 3: Calculate 12% of the result from Stage 2
Finally, we need to find 12% of 5,600. We multiply 5,600 by the decimal equivalent of 12%, which is 0.12, or by the fraction $\frac{12}{100}$.
So, 12% of 5,600 is 672.
Thus, 12% of 4% of 7% of $2 \times 10^6$ is 672.
Summary of Calculations
| Step | Calculation | Result |
|---|---|---|
| 1 | 7% of $2 \times 10^6$ | 140,000 |
| 2 | 4% of 140,000 | 5,600 |
| 3 | 12% of 5,600 | 672 |
The final result of the calculation is 672.
Final Answer Options
Comparing our result with the given options:
- Option 1: 386
- Option 2: 583
- Option 3: 672
- Option 4: 121
Our calculated value, 672, matches Option 3.
Revision Table: Key Concepts in Percentage Calculation
| Concept | Description |
|---|---|
| Percentage | A way of expressing a number as a fraction of 100. Represented by the symbol %. |
| Converting Percentage to Decimal | Divide the percentage by 100. E.g., 12% = 12/100 = 0.12. |
| Converting Percentage to Fraction | Write the percentage value over 100. E.g., 12% = 12/100. |
| Calculating "x% of y" | Multiply y by the decimal equivalent of x% (or by x/100). Formula: $\frac{x}{100} \times y$. |
| Percentage of Percentage | To calculate a percentage of a percentage of a number, calculate the percentages sequentially. For example, a% of b% of N = $\frac{a}{100} \times (\frac{b}{100} \times N)$. |
Additional Information: Understanding Powers of 10 and Percentages
Understanding powers of 10 makes working with large numbers easier. $10^6$ means 10 multiplied by itself 6 times, which is 1,000,000.
Percentage calculations are fundamental in many areas, including finance, statistics, and everyday life. When dealing with "percentage of percentage," it's crucial to calculate step by step. For instance, 10% of 10% of 100 is NOT 10% (which would be 10). It is (10/100) * ((10/100) * 100) = 0.1 * (0.1 * 100) = 0.1 * 10 = 1. Each percentage is applied to the *result* of the previous calculation, not the original number.
Important Questions from Percentage
A number p increased by p% of 99 equals 99 increased by 99% of p. What is (p + 51)% of 928 + 72?
Amina saves 16% of her income. Now her income is increased by 20% but she still saves the same amount as before. What is the percentage increase in her expenditure?
Vignesh spends 42% of his monthly salary on food, 16% on house rent, 11% on entertainment and 7% on conveyance. But due to some family function, he has to borrow Rs. 12,000 from a money leader to meet the expenses of Rs. 18,000 What is his monthly salary?
If X is 12.25% more than Y. then Y is approximately_____ less than X.
21% of a number is 546. What will be 89% of that number?
