Convert: 10 cm = ? m Convert your answer to scientific notation.
The Correct Answer and Explanation is:
Correct Answer:
10 cm = 0.1 m
In scientific notation: 1.0 × 10⁻¹ m
Explanation:
To convert centimeters (cm) to meters (m), you need to understand the relationship between these metric units. The metric system is based on powers of ten, which makes conversions straightforward when you know the correct ratio.
1 meter is equal to 100 centimeters.
This means:
1 m = 100 cm
Or inversely:
1 cm = 0.01 m
Step-by-Step Conversion:
We are given:
10 cm
To convert centimeters to meters, divide by 100: 10 cm÷100=0.1 m10 \, \text{cm} \div 100 = 0.1 \, \text{m}10cm÷100=0.1m
So, 10 cm = 0.1 meters.
Convert to Scientific Notation:
Scientific notation is a way to express numbers as a product of a number between 1 and 10 and a power of 10.
The number 0.1 can be written as: 0.1=1.0×10−10.1 = 1.0 \times 10^{-1}0.1=1.0×10−1
Thus: 10 cm=0.1 m=1.0×10−1 m10 \, \text{cm} = 0.1 \, \text{m} = 1.0 \times 10^{-1} \, \text{m}10cm=0.1m=1.0×10−1m
Why Use Scientific Notation?
Scientific notation is especially helpful in science and engineering because it:
- Makes very small or very large numbers easier to write and read.
- Clearly shows the scale or magnitude of a measurement.
- Reduces the risk of error in calculations involving extreme values.
For example, instead of writing 0.0000000567 m, you could write 5.67 × 10⁻⁸ m, which is cleaner and more precise.
Summary:
- 10 cm = 0.1 m
- In scientific notation: 1.0 × 10⁻¹ m
- Use scientific notation for clarity, precision, and efficiency in scientific communication.
