Consider these three numbers expressed in scientific notation: 2.4 × 104, 6.3 × 105, and 9.6 × 107. Which number is the greatest, and by how many times is it greater than the smallest number?
To determine which number is the greatest among the three, and how many times it is greater than the smallest number, we can compare their exponents.
The numbers expressed in scientific notation are:
1. 2.4 × 10^4
2. 6.3 × 10^5
3. 9.6 × 10^7
The number with the greatest exponent (or power of 10) will be the greatest. In this case, 9.6 × 10^7 has the highest exponent, so it is the greatest number among the three.
To calculate how many times the greatest number is greater than the smallest number, we need to divide the greatest number by the smallest number.
Smallest number: 2.4 × 10^4
Greatest number: 9.6 × 10^7
Dividing the greatest number by the smallest number:
(9.6 × 10^7) / (2.4 × 10^4) = (9.6 / 2.4) × (10^7 / 10^4) = 4 × 10^(7-4) = 4 × 10^3
Therefore, the greatest number is 4 times greater than the smallest number.