Question

which number sentence is correct? a. $31.009 < 31.07$ b. $32.06 < 32.060$ c. $44.050 < 40.55$ d. $54.02 < 54.004$

Explanation:

Step1: Analyze Option A

Compare the two decimals \(31.009\) and \(31.07\). The whole number parts are both \(31\). For the decimal parts, the tenths place is \(0\) for both. The hundredths place: \(0\) (from \(31.009\)) vs \(7\) (from \(31.07\)). Since \(0 < 7\), \(31.009<31.07\) is true.

Step2: Analyze Option B

Compare \(32.06\) and \(32.060\). According to the property of decimals, adding or removing trailing zeros after the decimal point doesn't change the value. So \(32.06 = 32.060\), so \(32.06<32.060\) is false.

Step3: Analyze Option C

Compare \(44.050\) and \(40.55\). The whole number part: \(44>40\), so \(44.050<40.55\) is false.

Step4: Analyze Option D

Compare \(54.02\) and \(54.004\). The whole number and tenths place are the same. The hundredths place: \(2\) (from \(54.02\)) vs \(0\) (from \(54.004\)). Since \(2 > 0\), \(54.02<54.004\) is false.

Answer:

A. \(31.009 < 31.07\)