Sure, let's break down the solution to this problem step by step.
### Part 1: Decrease 90 by 40%
1. Identify the initial value and the percentage decrease:
- Initial value = 90
- Percentage decrease = 40%
2. Calculate the amount decreased:
- The amount decreased is calculated by finding the percentage of the initial value.
[tex]\[
\text{Amount Decreased} = 90 \times \left(\frac{40}{100}\right) = 90 \times 0.40 = 36.0
\][/tex]
3. Calculate the decreased value:
- Subtract the amount decreased from the initial value to find the new value.
[tex]\[
\text{Decreased Value} = 90 - 36.0 = 54.0
\][/tex]
So, the amount decreased is 36.0 and the decreased value is 54.0.
### Part 2: Increase 1 m 10 cm by 5%
1. Convert the initial value to meters:
- Since we have 1 meter and 10 centimeters, we convert 10 cm to meters:
[tex]\[
10 \, \text{cm} = \frac{10}{100} \, \text{m} = 0.1 \, \text{m}
\][/tex]
- Add this to 1 meter:
[tex]\[
\text{Initial Value in Meters} = 1 \, \text{m} + 0.1 \, \text{m} = 1.1 \, \text{m}
\][/tex]
2. Identify the percentage increase:
- Percentage increase = 5%
3. Calculate the amount increased:
- The amount increased is found by calculating 5% of the initial value.
[tex]\[
\text{Amount Increased} = 1.1 \times \left(\frac{5}{100}\right) = 1.1 \times 0.05 = 0.055
\][/tex]
4. Calculate the increased value:
- Add the amount increased to the initial value to find the new value.
[tex]\[
\text{Increased Value} = 1.1 + 0.055 = 1.155
\][/tex]
So, the amount increased is 0.055 meters, and the increased value is 1.155 meters.
### Summary
- The amount decreased when decreasing 90 by 40% is 36.0, and the decreased value is 54.0.
- The amount increased when increasing 1 meter 10 centimeters by 5% is 0.055 meters, and the increased value is 1.155 meters.
I hope this breakdown helps you understand the steps involved in solving the problem.
