Carla used a calculator and found out that 31.5 \times 21.68=682.92. Explain to her why the answer is correct by reasoning about the size of the factors.

Carla used a calculator and found out that $$\displaystyle{31.5}\times{21.68}={682.92}$$. She is suspicious about her answer because it doesn't have three decimal places in it. Explain to her why the answer is correct by reasoning about the size of the factors, and also why her answer doesn't have $$\displaystyle{2}+{1}={3}$$ decimal places.

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Brittany Patton
Step 1
$$\displaystyle{31.5}\times{21.68}={682.92}$$
We know that $$\displaystyle{3}\times{2}={6}$$
Also, $$\displaystyle{30}\times{20}={600}$$
Thus solution should be $$\displaystyle{>}{600}$$.
Step 2
Also, 8 (which is the last decimal digit of 21.68) $$\displaystyle\times{5}$$ (which is the last decimal digit of 31.5) $$\displaystyle={40}$$. This 0 cancels the 3rd decimal digit in the answer. Thus, the solution has 2 decimal digits.