Question

level 150
what fraction and decimal is shown on this 1000 grid? select all that apply.
select multiple answers
a 0.1 + 0.01 + 0.001 = 0.111
b one hundred eleven thousandths
c \\(\frac{100}{1000} + \frac{10}{1000} + \frac{1}{1000} = \frac{111}{1000}\\)
d one and eleven hundredths

Explanation:

Step1: Analyze Option A

Calculate \(0.1 + 0.01 + 0.001\). \(0.1\) is tenths, \(0.01\) is hundredths, \(0.001\) is thousandths. \(0.1+0.01 = 0.11\), \(0.11 + 0.001=0.111\). So A is correct.

Step2: Analyze Option B

The decimal \(0.111\) is read as one hundred eleven thousandths (since the third decimal place is thousandths place, and \(0.111=\frac{111}{1000}\)). So B is correct.

Step3: Analyze Option C

\(\frac{100}{1000}\) is hundredths place (0.1), \(\frac{10}{1000}\) is thousandths? Wait, no: \(\frac{100}{1000}=0.1\) (tenths place? Wait, \(\frac{100}{1000}=0.1\) (1 tenth), \(\frac{10}{1000}=0.01\) (1 hundredth), \(\frac{1}{1000}=0.001\) (1 thousandth). So adding them: \(\frac{100 + 10+1}{1000}=\frac{111}{1000}\), which is correct. So C is correct.

Step4: Analyze Option D

"One and eleven hundredths" is \(1.11\), but our value is \(0.111\), not \(1.11\). So D is incorrect.

Answer:

A. \(0.1 + 0.01 + 0.001 = 0.111\), B. one hundred eleven thousandths, C. \(\frac{100}{1000}+\frac{10}{1000}+\frac{1}{1000}=\frac{111}{1000}\)