Question

write the statement in words, and determine whether it is true or false.

\\3.8 \ge 3.80\\

write the statement in words. choose the correct answer below.

a. three and eight-hundredths is less than three and eighty-hundredths.
b. three and eight-tenths is less than or equal to three and eighty-thousandths.
c. three and eight-tenths is greater than or equal to three and eighty-hundredths.
d. three and eight-thousandths is greater than three and eighty-hundredths.

is the statement true or false?

a. the statement is false because 3.8 is less than 3.80, and the inequality allows equality.
b. the statement is false because 3.8 is equal to 3.80, and the inequality does not allow equality.
c. the statement is true because 3.8 is equal to 3.80, and the inequality allows equality.
d. the statement is true because 3.8 is greater than 3.80.

Explanation:

Translate the mathematical statement into words

The given statement is \(3.8 \ge 3.80\).

• \(3.8\) is read as "three and eight-tenths".
• \(\ge\) is read as "is greater than or equal to".
• \(3.80\) is read as "three and eighty-hundredths".

Combining these gives: "Three and eight-tenths is greater than or equal to three and eighty-hundredths." This matches option C.

Evaluate the truth value of the statement

• Compare the values: \(3.8\) is mathematically equal to \(3.80\) because trailing zeros to the right of the decimal point do not change the value.
• The inequality symbol \(\ge\) means "greater than OR equal to". Since \(3.8 = 3.80\), the condition of being equal is satisfied.
• Therefore, the statement is true because \(3.8\) is equal to \(3.80\), and the inequality allows equality. This matches option C.

Answer:

Question 1

• (A) Three and eight-hundredths is less than three and eighty-hundredths.
• (B) Three and eight-tenths is less than or equal to three and eighty-thousandths.
• (C) Three and eight-tenths is greater than or equal to three and eighty-hundredths. (Correct answer)
• (D) Three and eight-thousandths is greater than three and eighty-hundredths.

Question 2

• (A) The statement is false because 3.8 is less than 3.80, and the inequality allows equality.
• (B) The statement is false because 3.8 is equal to 3.80, and the inequality does not allow equality.
• (C) The statement is true because 3.8 is equal to 3.80, and the inequality allows equality. (Correct answer)
• (D) The statement is true because 3.8 is greater than 3.80.