Question

husam tried to evaluate $16.8 \div 8$ using place value, but he made a mistake.
here is husams work.

step	work
step 1	168 hundredths $\div 8$
step 2	21 hundredths
step 3	$0.21$

what mistake did husam make?
choose 1 answer:
a $16.8$ is 168 tenths, not 168 hundredths.
b 168 hundredths $\div 8$ is 20 hundredths, not 21 hundredths.
c 21 hundredths is $2.1$, not $0.21$.

Explanation:

To determine Husam's mistake, we analyze the place value of 16.8. Let's break down 16.8:

• The digit 8 is in the tenths place, so 16.8 can be written as \(16 + 0.8\).
• Converting to tenths: \(16=\frac{160}{10}\) and \(0.8 = \frac{8}{10}\), so \(16.8=\frac{160 + 8}{10}=\frac{168}{10}\), which means 16.8 is 168 tenths.
• Husam incorrectly represented 16.8 as 168 hundredths (which would be \(1.68\), since \(\frac{168}{100}=1.68\)).
• Option B is incorrect because \(168\div8 = 21\), so 168 hundredths \(\div8\) is indeed 21 hundredths.
• Option C is incorrect because 21 hundredths is \(0.21\) (since \(\frac{21}{100}=0.21\)), not \(2.1\) (which is 21 tenths).

Thus, the mistake is in the place - value representation of 16.8.

Answer:

A. 16.8 is 168 tenths, not 168 hundredths.