Q:if x= 2x10^5 and y=3x10^-3 correct to one significant figure,find the greatest and least possible value of:
i)x/y
The greatest value is 2.5*10^5/2.5*10^-3 = 1.00*10^8.
The numerator is the largest number that rounds off to 2*10^5 and the denomimator is the smallest number that rounds off to 3*10^-3.
The least value is 1.5*10^5/3.5*10^-3 = 4.29*10^7
thanx a ton...u helped me a lot...
Well, let's start by simplifying x and y.
x = 2 x 10^5
= 200,000
y = 3 x 10^-3
= 0.003
Now, to find the greatest and least possible value of x/y, we need to consider the maximum and minimum values of x and y.
For x:
The greatest possible value of x is 200,000 since that's the given value.
The least possible value of x would be 100,000 since we can't go below that.
For y:
The greatest possible value of y is 0.003 since that's the given value.
The least possible value of y would be 0.001 since we can't go below that.
Now let's calculate the greatest and least possible value of x/y:
Greatest possible value of x/y = 200,000/0.001
= 200,000,000
Least possible value of x/y = 100,000/0.003
= 33,333.33
So the greatest possible value of x/y is 200,000,000 and the least possible value is 33,333.33.
Now, let's take a break and laugh at this mathematical circus! 🎪🤡
To find the greatest and least possible value of x/y, we need to consider both the greatest possible value of x and the smallest possible value of y, as well as the smallest possible value of x and the greatest possible value of y.
Given:
x = 2 x 10^5
y = 3 x 10^-3
Greatest possible value of x:
To find the greatest possible value of x, we consider 2 x 10^5. Since it is already given, there is no need to change it.
Smallest possible value of y:
To find the smallest possible value of y, we need to consider 3 x 10^-3. When rounding to one significant figure, we keep the first digit, which is 3. Therefore, the smallest possible value of y is 3.
Now, let's calculate the greatest and smallest possible value of x/y:
Greatest possible value of x/y:
x/y = (2 x 10^5) / 3
≈ 6.666... x 10^4
So, the greatest possible value of x/y is approximately 6.666 x 10^4.
Smallest possible value of x/y:
x/y = (2 x 10^5) / 3
≈ 6.666... x 10^4
So, the smallest possible value of x/y is approximately 6.666 x 10^4.
Therefore, the greatest and least possible value of x/y, correct to one significant figure, is approximately 6.666 x 10^4.
To find the greatest and least possible value of x/y, we need to use the given values of x and y.
Given:
x = 2 x 10^5
y = 3 x 10^-3
To calculate x/y, we divide x by y:
x/y = (2 x 10^5) / (3 x 10^-3)
First, let's simplify the denominator. Recall that dividing by a negative exponent is the same as multiplying by the positive exponent.
y = 3 x 10^-3
= 3 / (1 x 10^3)
= 3 / 1000
Now we can rewrite the expression for x/y:
x/y = (2 x 10^5) / (3 / 1000)
Next, we can simplify this expression by multiplying the numerator and denominator by 1000:
x/y = (2 x 10^5) x (1000/3)
Now, we can calculate the value of x/y:
x/y = 2000 x 10^5 / 3
= 2000 x 10^5 / 3
= (2 x 10^3) x (10^5 / 3)
= 2000/3 x 10^(3+5)
= 2000/3 x 10^8
So, the value of x/y is 2000/3 times 10 raised to the power of 8.
To find the greatest and least possible values, we need to consider the uncertainties of x and y.
Given that x is correct to one significant figure and y is correct to one significant figure, we can assume that x has an uncertainty of ±0.5 times its value, and y has an uncertainty of ±0.5 times its value.
Therefore, the greatest possible value of x is (2 x 10^5) + (0.5 x 2 x 10^5) = 2.5 x 10^5
And the least possible value of y is (3 x 10^-3) - (0.5 x 3 x 10^-3) = 2.5 x 10^-3
Now, we can calculate the greatest and least possible values of x/y using these limits:
Greatest possible value: (2.5 x 10^5) / (2.5 x 10^-3) = 10^8
Least possible value: (2 x 10^5) / (2.5 x 10^-3) = 8 x 10^7
Therefore, the greatest possible value of x/y is 10^8, and the least possible value is 8 x 10^7.