(a) By rounding each number in the calculation correct to 1 significant figure, work out an estimate for the value of A.
A = (136 + 47.2) / (62.9 - 18.1)
Show all your working.
(b) Use your calculator to find the actual value of A, correct to 4 significant figures.
(c) Write 2.37 × 10^6 as an ordinary number.
(d) Write 0.00045 in standard form.
(e) Calculate 3.5 × 10^7 + 4.4 × 10^5. Give your answer in standard form.
Answer (2)
The estimated value of A, after rounding, is approximately 3.75, and the actual value calculated is 4.093. The ordinary number for 2.37 × 10^6 is 2,370,000, and in standard form, 0.00045 is 4.5 × 10^{-4}. Lastly, the sum of 3.5 × 10^7 and 4.4 × 10^5 in standard form is 3.544 × 10^7.
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Sure! Let's solve each part of the question step-by-step:
(a) To estimate A by rounding each number to 1 significant figure, we approach the calculation as follows:
The number 136 rounds to 100.
The number 47.2 rounds to 50.
The number 62.9 rounds to 60.
The number 18.1 rounds to 20.
Putting these rounded numbers into the formula: A ≈ 60 − 20 100 + 50 = 40 150
Simplifying this gives: A ≈ 40 150 = 3.75
(b) To find the actual value of A using a calculator and correct to 4 significant figures:
Calculate the numerator: 136 + 47.2 = 183.2
Calculate the denominator: 62.9 - 18.1 = 44.8
Thus, the actual value of A is: A = 44.8 183.2 ≈ 4.090 (rounded to 4 significant figures).
(c) Write 2.37 × 1 0 6 as an ordinary number:
This is equivalent to multiplying 2.37 by 1,000,000.
Thus, 2.37 × 1 0 6 = 2 , 370 , 000 .
(d) Write 0.00045 in standard form:
To express this in standard form, move the decimal point 4 places to the right: 4.5 × 1 0 − 4 .
(e) Calculate 3.5 × 1 0 7 + 4.4 × 1 0 5 and give the answer in standard form:
Convert 4.4 × 1 0 5 to the same power of 10 as 3.5 × 1 0 7 , i.e., 0.044 × 1 0 7 .
Add them: 3.5 × 1 0 7 + 0.044 × 1 0 7 = ( 3.5 + 0.044 ) × 1 0 7 = 3.544 × 1 0 7 .
I hope this helps! Please feel free to ask any questions you might have.
