Final answer:
In long division, subtracting 7 from 9 helps determine how many times the divisor fits into the first digit of the dividend. The outcome also indicates the remainder, which is used in subsequent steps. This ties into the concept of significant figures, as accuracy and precision in calculations depend on understanding and applying these rules correctly.
Step-by-step explanation:
The subtraction of 7 from 9 in the context of long division is a part of the division algorithm. When we divide 917 by 7, we start by determining how many times 7 fits into the first digit, 9. Subtracting 7 from 9 shows us that 7 fits into 9 one time with a remainder. The result of the subtraction (9 - 7 = 2) tells you how much is left after subtracting 7 once from 9, and this remainder is then used in the next step of the division process when it is combined with the next digit of the dividend.
Understanding long division and manipulating numbers requires the knowledge of significant figures, especially when dealing with the results from a calculator. Significant figures are the digits that carry meaning contributing to its precision. This is pertinent when performing mathematical operations, as there are specific rules for limiting the number of significant figures in an answer: one rule for addition and subtraction, and another for multiplication and division.