Daniel has two pieces of string. String A is 3.4 meters long and String B is 2.75 meters long. Use >, <, or = to compare the two lengths. Which piece of string is longer? Colton ha... Daniel has two pieces of string. String A is 3.4 meters long and String B is 2.75 meters long. Use >, <, or = to compare the two lengths. Which piece of string is longer? Colton has a piece of string 2 4/5 meters long. He tells Daniel that his string is shorter than String B because 4 is less than 75. Explain how to correct Colton’s reasoning. Order the three lengths from longest to shortest. Read more

Steps to Solve

1. Compare the lengths of String A and String B

First, we need to compare the lengths of String A (3.4 meters) and String B (2.75 meters).

Convert them to the same format for easier comparison:

• String A: $3.4$ meters
• String B: $2.75$ meters

Since $3.4 > 2.75$, we can express this with the inequality: $$ 3.4 > 2.75 $$

2. Determine which string is longer

Given the comparison from step 1, we know that String A is longer than String B.

So, we conclude:

• String A is longer than String B, or: $$ \text{String A} > \text{String B} $$

3. Convert Colton's string length to a decimal

Colton's string is given as $2\frac{4}{5}$ meters. We need to convert this to a decimal to properly compare it.

Convert the mixed number: $$ 2\frac{4}{5} = 2 + \frac{4}{5} = 2 + 0.8 = 2.8 \text{ meters} $$

4. Compare Colton's string with String B

Now, we need to compare Colton's string (2.8 meters) with String B (2.75 meters).

Here, we compare: $$ 2.8 > 2.75 $$

Hence, Colton's string is longer than String B.

5. Order the three strings

List the lengths:

• String A: $3.4$ meters
• Colton's string: $2.8$ meters
• String B: $2.75$ meters

From longest to shortest, we order them as follows: $$ \text{String A} > \text{Colton's string} > \text{String B} $$