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Which of the following expressions is equivalent to $0.12 \times 0.7$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $12 \times 7 \div 10$ $\newline$ (B) $12 \times 7 \div 100$ $\newline$ (C) $12 \times 7 \div 1,000$ $\newline$ (D) $12 \times 7 \div 10,000$

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Division patterns with zeros

Full solution

Q. Which of the following expressions is equivalent to

0.12 \times 0.7

?

\newline

Choose

1

answer:

\newline

(A)

12 \times 7 \div 10

\newline

(B)

12 \times 7 \div 100

\newline

(C)

12 \times 7 \div 1,000

\newline

(D)

12 \times 7 \div 10,000

Convert to Fractions: To find an equivalent expression for $0.12 \times 0.7$ , we need to express the decimals as fractions and then simplify. $\newline$ $0.12$ can be written as $\frac{12}{100}$ because there are two decimal places, moving the decimal two places to the right turns it into a whole number ( $12$ ) and the denominator becomes $100$ . $\newline$ $0.7$ can be written as $\frac{7}{10}$ because there is one decimal place, moving the decimal one place to the right turns it into a whole number ( $7$ ) and the denominator becomes $10$ . $\newline$ Now we multiply the two fractions: $(\frac{12}{100}) \times (\frac{7}{10})$ .
Multiply Fractions: Next, we multiply the numerators together and the denominators together: $\newline$ $(12 \times 7) / (100 \times 10)$ . $\newline$ This simplifies to $84 / 1000$ .
Simplify Result: We can see that $84 / 1000$ is the same as dividing $84$ by $1000$ , which is the same as multiplying $0.084$ by $10$ to shift the decimal place one position to the right. $\newline$ So, $84 / 1000$ is equivalent to $0.084$ , which is the same as $0.12 \times 0.7$ .
Check Given Options: Now, we need to match our result with the given options: $\newline$ (A) $12 \times 7 \div 10 = 84 \div 10 = 8.4$ (which is not equivalent to $0.084$ ) $\newline$ (B) $12 \times 7 \div 100 = 84 \div 100 = 0.84$ (which is not equivalent to $0.084$ ) $\newline$ (C) $12 \times 7 \div 1,000 = 84 \div 1,000 = 0.084$ (which is equivalent to $0.084$ ) $\newline$ (D) $12 \times 7 \div 10,000 = 84 \div 10,000 = 0.0084$ (which is not equivalent to $0.084$ )
Choose Correct Answer: Therefore, the correct answer is $(C) 12 \times 7 \div 1,000$ .

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