Question

which decimal is equal to 181.5 ÷ (-100)? a 0.1815 b -0.1815 c 1.815 d -1.815

Explanation:

Step1: Recall division by 100 rule

Dividing a number by 100 moves the decimal point two places to the left. For \(181.5\div100\), we move the decimal in \(181.5\) two places left: \(1.815\).

Step2: Consider the negative sign

The problem is \(181.5\div(-100)\). The sign rule for division: positive \(\div\) negative = negative. So \(181.5\div(-100)= - (181.5\div100)= - 1.815\)? Wait, no, wait. Wait, \(181.5\div100\): \(181.5\) has decimal after 1, moving two left: \(1.815\)? Wait, no, \(181.5\) is 181 and 5 tenths. Dividing by 100: \(181.5\div100 = 1.815\)? Wait, no, \(181.5\div10 = 18.15\), \(181.5\div100 = 1.815\)? Wait, no, wait, 100 times 1.815 is 181.5? Let's check: \(1.815\times100 = 181.5\), yes. But the divisor is -100. So \(181.5\div(-100)= - (181.5\div100)= - 1.815\)? Wait, but let's re - evaluate. Wait, \(181.5\div100\): moving decimal two places left. 181.5: the decimal is after 1 (181.5). Moving two places left: first place left: 18.15 (divided by 10), second place left: 1.815 (divided by 100). So \(181.5\div100 = 1.815\), then with the negative sign, \(181.5\div(-100)= - 1.815\). Wait, but let's check the options. Option D is -1.815. Wait, did I make a mistake earlier? Wait, let's do the division: \(181.5\div(-100)=\frac{181.5}{-100}=-1.815\). Yes, because \(181.5\div100 = 1.815\), so dividing by -100 gives -1.815. So the correct option is D. Wait, but let's check the options again. Option D is -1.815. So that's the answer.

Wait, maybe I messed up the decimal movement. Let's do it step by step. \(181.5\div(-100)\). Dividing by 100: shift decimal two places left. 181.5 → 1.815 (after shifting two left: 1 (hundreds place), 8 (tens), 1 (ones),. (decimal), 5 (tenths)? Wait, no. Wait, 181.5 is 1×100 + 8×10 + 1×1 + 5×0.1. Dividing by 100: each digit's place value is divided by 100. So 1×100÷100 = 1×1, 8×10÷100 = 8×0.1, 1×1÷100 = 1×0.01, 5×0.1÷100 = 5×0.001. Wait, no, that's not the right way. The correct way to divide a decimal by 100 is to move the decimal point two places to the left. So 181.5: decimal is between 1 and 5 (181.5). Moving two places to the left: first, move one place left: 18.15 (divided by 10), second place left: 1.815 (divided by 100). So \(181.5\div100 = 1.815\), then with the negative sign, \(181.5\div(-100)= - 1.815\), which is option D.

Answer:

D. \(-1.815\)