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Chapter 8: Problem 3

Complete. Do as much as possible mentally. a) 1 dam = ______ m b) 1 m = ______dam

Short Answer

Expert verified
a) 1 dam = 10 m, b) 1 m = 0.1 dam

Step by step solution

01

Understand the Conversion Factor

1 decameter (dam) is equal to 10 meters (m). In other words, 1 dam = 10 m. This is a standard conversion factor.
02

Solve Part (a)

Using the conversion factor, we can directly write: 1 dam = 10 m.
03

Solve Part (b)

To find the conversion from meters to decameters, use the relation that 1 dam = 10 m. Therefore, to convert meters to decameters, you divide by 10. Hence, 1 m = 1/10 dam or 0.1 dam.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

decameter to meter conversion
When converting from decameters (dam) to meters (m), it's important to know that 1 decameter equals 10 meters. This is a fixed conversion factor.

To convert decameters to meters, simply multiply the number of decameters by 10. For example, if you have 2 dam, you multiply by 10 to get 20 m.

Here's a formula to help:

\[ \text{meters} = \text{decameters} \times 10 \]

So if you have 1 dam, using the formula we get:
\[ 1 \text{ dam} \times 10 = 10 \text{ m} \]

This can be done mentally once you get the hang of it since you are simply adding a zero to the original number.
meter to decameter conversion
Converting from meters (m) to decameters (dam) involves doing the reverse of what we did earlier. Since 1 decameter equals 10 meters, to find how many decameters are in a meter, we divide by 10.

To put it in simpler terms, for every 10 meters, you get 1 decameter. So if you have 20 meters, you would divide by 10 to get 2 decameters.

Use the formula:

\[ \text{decameters} = \frac{\text{meters}}{10} \]

For example, if you have 1 meter and you want to convert it to decameters:
\[ 1 \text{ m} \times \frac{1}{10} = 0.1 \text{ dam} \]

It's a useful trick to remember that dividing by 10 in your head is like moving the decimal point one place to the left.
basic mathematical operations
Understanding basic mathematical operations is crucial when tackling any kind of conversion. Here are some tips for handling multiplication and division by 10, which are often required when working with metric conversions.

For multiplication by 10:
  • Simply add a zero to the end of the number.

    Example: 3 x 10 = 30.
For division by 10:
  • Move the decimal point one place to the left.

    Example: 25 梅 10 = 2.5.
These operations are simple but very powerful when dealing with metric units.

Always double-check your conversions to ensure accuracy. Use these fundamental operations to confidently convert between units such as meters and decameters.

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