Question

The distance \(10.5 \mathrm{~cm}\) could also be expressed as

Short answer

The distance \(10.5~\mathrm{cm}\) can also be expressed as \(0.105~\mathrm{m}\) or \(105~\mathrm{mm}\).

Step-by-step solution

1. Understand the problem

We are given a distance of 10.5 cm, and our task is to express that distance in different units of length, such as meters (m) and millimeters (mm).

2. Know the conversion factors

To convert among different units of length, we need to know the following conversion factors: 1. 1 meter (m) is equal to 100 centimeters (cm). 2. 1 centimeter (cm) is equal to 10 millimeters (mm).

3. Convert from centimeters to meters

First, let's convert the given distance from centimeters (cm) to meters (m). Recall that 1 meter is equal to 100 centimeters. To convert from centimeters to meters, we need to divide the given distance by the conversion factor. In this case, we have: \( \frac{10.5~\mathrm{cm}}{100~\mathrm{cm/m}} = 0.105~\mathrm{m} \) So, 10.5 cm is equal to 0.105 m.

4. Convert from centimeters to millimeters

Now, let's convert the given distance from centimeters (cm) to millimeters (mm). Recall that 1 centimeter is equal to 10 millimeters. To convert from centimeters to millimeters, we need to multiply the given distance by the conversion factor. In this case, we have: \( 10.5~\mathrm{cm} \times 10~\mathrm{mm/cm} = 105~\mathrm{mm} \) So, 10.5 cm is equal to 105 mm. Thus, the distance 10.5 cm can also be expressed as 0.105 m or 105 mm.

Key concepts

Centimeters to Meters

Converting centimeters to meters is a common process in length conversion. It helps in understanding measurements in different units that are standard in various situations. To convert centimeters to meters, you need to use the conversion factor:

• 1 meter is equivalent to 100 centimeters.

This conversion factor implies that there are 100 centimeters in every meter. Thus, when converting from centimeters to meters,
you simply divide the centimeter value by 100. For instance, to convert 10.5 centimeters (cm) to meters (m):\[ \frac{10.5\,\text{cm}}{100} = 0.105\,\text{m} \]The formula turns centimeters into meters by scaling down the value. 0.105 meters is more suitable for larger measurements, such as room dimensions. It's important to remember this method so that you can effortlessly switch between units when needed.

Centimeters to Millimeters

Converting centimeters to millimeters is usually more straightforward, because the units are closer in value. Remember that:

• 1 centimeter is equal to 10 millimeters.

This conversion factor means that converting from centimeters to millimeters involves a straightforward multiplication. You multiply the number of centimeters by 10 to get the number of millimeters.
For example, turning 10.5 cm into millimeters would be:\[ 10.5\,\text{cm} \times 10 = 105\,\text{mm} \]This straightforward math is essential when dealing with very small objects or precise measurements.
Converting to millimeters can be helpful in fields where smaller units provide better precision. Always remember to multiply when converting from centimeters to millimeters.

Length Conversion

Length conversion is an essential skill in various fields, from scientific research to everyday measurements in construction and more. Understanding how to switch seamlessly between units involves knowing the standard conversion factors. Some key points include:

• Using 100 to convert from centimeters to meters, which simplifies by dividing.
• Utilizing 10 to move from centimeters to millimeters, which simplifies by multiplying.

The ability to convert between different units will let you interpret data correctly and make better-informed decisions. Having this knowledge ensures that you don't make costly mistakes due to unit errors.
Understanding these conversion techniques can aid in entrepreneurial activities, scientific experiments, academic learning, and daily problem-solving.