Question

Amelia's school has (1 x 10°) + (2 X 10') + (5 x 1) students. Luke's school has (9 X 10^) + (6 X 10') + (4 X 1) students. Without computing, how could you decide which school has more students?

Answer 1

To determine which school has more students without computing the actual numbers, compare the highest place value in the numbers provided for each school. Luke's school has a larger coefficient at the highest place value (10²), indicating it has more students than Amelia's school.

Step-by-step explanation:

To decide which school has more students without computing, we can compare the numbers based on the highest place value. Both Amelia's and Luke's schools' student numbers are given in a base 10 format where the highest place value dictates the largest contribution towards the total.

Amelia's school has (1 × 10²) + (2 × 10¹) + (5 × 1), and Luke's school has (9 × 10²) + (6 × 10¹) + (4 × 1). Given that the coefficients of 10² for Luke's school is higher (9 vs. 1), and since 10² represents the largest place value (the hundreds place), Luke's school inherently has more students.

The scientific notation and understanding of place value in exponent form can help us determine the larger number without explicit calculations. Specifically, a larger coefficient at a higher power of 10 indicates a larger overall value.