Calculate $$ 10 \% $$ of the following numbers: 3000,40 and 1200 Calculate the percentage increase of decrease.

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UpStudy AI · Accepted Answer

**Step 1. Calculate 10% of each number**

To find 10% of a number, we multiply the number by $$0.10$$ (or $$\frac{10}{100}$$).

- For $$3000$$:
  $$
  10\%\ \text{of}\ 3000 = 0.10 \times 3000 = 300
  $$

- For $$40$$:
  $$
  10\%\ \text{of}\ 40 = 0.10 \times 40 = 4
  $$

- For $$1200$$:
  $$
  10\%\ \text{of}\ 1200 = 0.10 \times 1200 = 120
  $$

**Step 2. Calculate the percentage decrease when going from the original number to its 10% value**

When a number is reduced to 10% of its original value, the decrease is the difference between the original value and the 10% value. The percentage decrease is computed by:
$$
\text{Percentage decrease} = \frac{\text{Original} - \text{New}}{\text{Original}} \times 100\%
$$

For any number in this case:
- The new value is $$10\%$$ of the original.
- The difference is:
  $$
  \text{Difference} = \text{Original} - 0.10 \times \text{Original} = 0.90 \times \text{Original}
  $$
- Thus, the percentage decrease is:
  $$
  \frac{0.90 \times \text{Original}}{\text{Original}} \times 100\% = 90\%
  $$

So, for each of the numbers (3000, 40, and 1200) the decrease from the original value to 10% of the original is a $$90\%$$ decrease.

**Step 3. Calculate the percentage increase when going from the 10% value back to the original number**

To return from the reduced number (which is 10% of the original) to the original, we need to determine what percentage increase that requires. The percentage increase is given by:
$$
\text{Percentage increase} = \frac{\text{Original} - \text{Reduced}}{\text{Reduced}} \times 100\%
$$

Since for any original number:
- $$\text{Reduced} = 0.10 \times \text{Original}$$,
- The difference is:
  $$
  \text{Original} - \text{Reduced} = \text{Original} - 0.10 \times \text{Original} = 0.90 \times \text{Original}
  $$
- Then:
  $$
  \text{Percentage increase} = \frac{0.90 \times \text{Original}}{0.10 \times \text{Original}} \times 100\% = \frac{0.90}{0.10} \times 100\% = 9 \times 100\% = 900\%
  $$

So, to go from the 10% value back to the original number, a $$900\%$$ increase is needed.

**Summary of Answers:**

- **10% Values:**
  - $$3000$$ becomes $$300$$
  - $$40$$ becomes $$4$$
  - $$1200$$ becomes $$120$$

- **Percentage Decrease:**  
  Each original number is reduced by $$90\%$$ when taken down to its 10% value.

- **Percentage Increase:**  
  Increasing the 10% value back to the original number requires a $$900\%$$ increase.
- 10% of 3000 is 300, 40 is 4, and 1200 is 120. - Each number decreases by 90% when reduced to 10%. - To increase 10% back to the original, a 900% increase is needed.

Calculate \( 10 \% \) of the following numbers: 3000,40 and 1200 Calculate the percentage increase of decrease.

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