Problem 26 - Introductory Chemistry Atoms First

Question

\(1555 \mathrm{~cm}+0.001 \mathrm{~cm}+0.8 \mathrm{~cm}=?\)

Step-by-Step Solution

Answer

\(1555.801 \mathrm{~cm}\)

Step 1: Convert all given lengths into decimals

We have 3 lengths to add: 1555 cm, 0.001 cm, and 0.8 cm. The first and the last lengths are already in decimal form, so we don't need to convert them.

Step 2: Add the given lengths

Now that we have all the lengths in decimal form, we can add them easily: \(1555 \mathrm{~cm} + 0.001 \mathrm{~cm} + 0.8 \mathrm{~cm}\)

Step 3: Perform the addition

Adding the three lengths, we get: \(1555.001 \mathrm{~cm} + 0.8 \mathrm{~cm} = 1555.801 \mathrm{~cm}\)

Step 4: Write the final answer

The total length, which is the sum of the given lengths, is 1555.801 cm.

Key Concepts

Decimal Conversion

Decimals make it easy to express fractions in a clear manner. When adding or subtracting values with decimals, it's important to ensure all numbers are in the same format.
For the example given, we see some numbers already in decimal form:

• 1555 is a whole number, also viewed as 1555.0, a decimal.
• 0.8 is also a decimal and needs no conversion.
• 0.001 is already in a fine decimal format as well.

Thus, the given quantities do not need any further decimal conversion before addition. However, understanding how to handle numbers in decimal or fractional form is crucial in math problems. This involves aligning the decimal points and considering any necessary changes to fractions.

Mathematics Problem Solving

Problem-solving in mathematics often involves a series of logical steps to get to a solution. In the exercise with decimals, the correct procedure is clear and systematic.
First, ensure all numbers are in compatible forms before any operation. This could involve decimal conversion, if needed. In our exercise, this step was simple since all lengths were provided in decimals.
Next, add the decimal numbers by stacking them to align the decimal points. For instance:

• 1555.001
• + 0.800

When solved step-by-step, these values were easily summed to reach a final result of 1555.801 cm. It's crucial to follow such structured processes for accuracy.

Unit Conversion

Unit conversion is the process of changing measurements from one unit to another. While the exercise provided only units of centimeters, understanding unit conversion's importance remains significant.
In mathematics and science, lengths might need conversion from centimeters to meters, or vice-versa. Knowing how 1 meter equals 100 centimeters can simplify this process. To convert 1555.801 cm to meters:

• Divide the centimeter value by 100.
• Thus, 1555.801 cm becomes 15.55801 meters.

The ability to convert units is essential, enabling understanding across diverse fields and ensuring measurements are accurate and relevant to the situation.