Final answer:
The lower bound of x - y, when x = 6.7 x 10^7 and y = 1.3 x 10^6 rounded to two significant figures, is approximately 6.5 x 10^7 in standard form.
Step-by-step explanation:
To calculate the lower bound of x - y, we must consider what the lowest possible value of x and the highest possible value of y could be based on their significant figures when rounded. Since x is rounded to two significant figures as 6.7 × 10^7, the smallest value x could be is half of the place value of the last significant figure lower, so x ≅ 6.65 × 10^7. Similarly, y, rounded to 1.3 × 10^6, could be up to 1.35 × 10^6.
Therefore, we subtract the upper estimate for y from the lower estimate for x to find the lower bound of x - y.
The calculation is as follows:
- x (lower estimate) ≅ 6.65 × 10^7
- y (upper estimate) ≅ 1.35 × 10^6
- Lower bound of x - y = (6.65 × 10^7) - (1.35 × 10^6)
To subtract these values in standard form, we write them with the same exponent:
- y (upper estimate) in terms of 10^7: 1.35 × 10^6 = 0.135 × 10^7
- Lower bound of x - y = (6.65 - 0.135) × 10^7
- Lower bound of x - y ≅ 6.515 × 10^7
This gives us the lower bound in standard form as approximately 6.5 × 10^7.