calculate the upper and lower bounds of the following calculations given that each number is written to the nearest whole number
40o divided by 60
10 times 9 multipiled by 1
To calculate the upper and lower bounds of these calculations, we need to consider the rounding error introduced by rounding each number to the nearest whole number.
1. 40 divided by 60:
To find the upper bound, we need to round the numerator and denominator up to the nearest whole number. Since 40 is already a whole number, there is no rounding error for the numerator. However, 60 would be rounded up to 61. So the upper bound would be 40 divided by 61.
To find the lower bound, we need to round the numerator and denominator down to the nearest whole number. Again, 40 is already a whole number with no rounding error. The denominator 60 would be rounded down to 59. So the lower bound would be 40 divided by 59.
2. 10 times 9 multiplied by 1:
In this calculation, all the numbers are already whole numbers. So there is no rounding error introduced. Therefore, both the upper and lower bounds would simply be the calculation itself, which is 10 times 9 multiplied by 1.
To summarize:
1. The upper bound for 40 divided by 60 is 40 divided by 61.
2. The lower bound for 40 divided by 60 is 40 divided by 59.
3. The upper and lower bounds for 10 times 9 multiplied by 1 are both equal to the calculation itself, which is 10 times 9 multiplied by 1.