The place value of $9$ in $0.06945$ is

### Concept & Strategy In a decimal number, the place value of a digit is determined by its position relative to the decimal point. The first position to the right is tenths ($\frac{1}{10}$), the second is hundredths ($\frac{1}{100}$), the third is thousandths ($\frac{1}{1000}$), and so on. ### Step-by-Step Solution * **Given:** The decimal number $0.06945$. * **Positional Analysis:** Let's map out the digits after the decimal point: 1st place (0): Tenths ($\frac{0}{10}$) 2nd place (6): Hundredths ($\frac{6}{100}$) 3rd place (9): Thousandths ($\frac{9}{1000}$) * **Conclusion:** The digit $9$ sits in the third decimal place. Therefore, its place value is $9$ thousandths. $$\frac{9}{1000}$$ ### Exam Strategy & Shortcut Count the position of the target digit directly from the decimal point. The digit $9$ is $3$ spaces to the right. Therefore, the denominator of its place value fraction must have exactly $3$ zeros ($1000$). Match this instantly with option (d). ### Common Pitfall Students often confuse decimal place names with whole number place names (tens, hundreds, thousands) and might shift their counting by one position. Remember that decimals start at "tenths," not "oneths." ### Final Answer **Therefore, the correct answer is $\frac{9}{1000}$.**