The product of $0.09$ and $0.007$ is

### Concept & Formula When multiplying decimals, the number of decimal places in the final product is exactly equal to the sum of the decimal places in the individual numbers being multiplied. ### Step-by-Step Solution **Given:** $0.09$ and $0.007$ First, multiply the non-zero integer parts: $9 \times 7 = 63$ Next, count the decimal places in the original numbers: $0.09$ has $2$ decimal places. $0.007$ has $3$ decimal places. Total decimal places required = $2 + 3 = 5$. Shift the decimal point $5$ places to the left from the integer $63$: $0.00063$ ### Exam Strategy & Shortcut Simply count the decimal places mentally. $2$ places plus $3$ places equals $5$ places. Quickly scan the options for the number with exactly $5$ decimal places. Option (b) is $0.00063$ (which has $5$). Option (d) has $6$. ### Common Pitfall Miscounting the placeholder zeros. Students often just see "two zeros" in the first number and "two zeros" in the second number and guess blindly, forgetting that the digits $6$ and $3$ also count towards the total decimal place tally. ### Final Answer Therefore, the correct answer is $0.00063$.