Final answer:
The task involves matching rational numbers to their equivalent decimal expansions by performing division. Correct matches are a) 7/15 with 0.46, c) 7/8 with 0.875, and d) 7/10 with 0.7. Option b) 7/9 does not match with 0.7.
Step-by-step explanation:
The student's question involves expressing rational numbers in their decimal expansion form. To find the decimal expansion, you can divide the numerator by the denominator. Let's match each rational number to its equivalent decimal expansion:
a) 7/15 - To find the decimal expansion, divide 7 by 15 which gives you approximately 0.4666..., so it can be rounded to 0.47. Therefore, 7/15 matches with 0.46 if rounded to two decimal places.
b) 7/9 - Dividing 7 by 9 gives you 0.777, which is a repeating decimal that can be rounded to 0.7777. Thus, 7/9 does not match with 0.7 as it rounds to 0.78.
c) 7/8 - When you divide 7 by 8, you get 0.875, which is the exact decimal expansion. So, 7/8 perfectly matches with 0.875.
d) 7/10 - This is the same as saying 0.7, because 7/10 is the decimal 0.7. So, 7/10 matches with 0.7 exactly.
To summarize, the correct matches are a) 7/15 - 0.46, c) 7/8 - 0.875, and d) 7/10 - 0.7. Option b) does not match with any given decimal expansion