Calculation+exercises+-+Corrections
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School
University of Ontario Institute of Technology *
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Course
1010U
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
2
Uploaded by KidMinkMaster1019
Practice exercises: Rounding numbers, scientific notation, conversion of units 1. Write the following numbers in scientific notations, rounding to one number after the decimal point a. 0.000278: _______
2.8 x 10
-4
_________________________________ b. 1,479 x 10
-3
: _______
1.5
_________________________________ c. 0.00621 x 10
6
: _______
6.2 x 10
3
______________________________ d.: 2,150,000: _______
2.2 x 10
6
_______________________________ 2.
Convert the following into full numbers a.
0.000578 x 10
4
: _________
5.78
___________________________ b.
1,490.8 x 10
-6
: ______
0.0014908
______________________________ c.
357 x 10
2
: _______
35700
_____________________________ d.
0.88765 x 10
-3
: _______
0.00088765
____________________________ 3. Perform the following calculations; report the final number using scientific notation rounding to one number after the decimal point a. Add 8.56x10
2 + 0.092x10
4
(show the detail of the calculation) 8.58 x 10
2 + 0.092x10
4
= 8.58 x 10
2 + 9.2 x 10
2 = (8.58
+ 9.2) x 10
2
= 17.78 x 10
2
= 1.8 x 10
3
b. Multiply 8x10
2
x 2x10
4
(show the detail of the calculation) 8x10
2
x 2x10
4 =
(8 x 2) x 10
(2+4)
= 16 x 10
6
= 1.6
x 10
7
c.
Subtract 0.76x10
4
–
1.34x10
3 (show the detail of the calculation) 0.76 x10
4
–
1.34 x10
3 =
7.6 x10
3
–
1.34 x10
3
=
(7.6 –
1.34) x10
3 = 6.26 x10
3
= 6.3 x10
3
d.
Divide 6 x 10
-6 (show the detail of the calculation) 3 x 10
-7 6 x 10
-6 \ 3 x 10
-7
= 6 / 3 x 10
(-6 –
(-7)) = 2 x 10
(-6 + 7))
= 2.0 x 10
1
4. Perform the following conversion; write the final numbers in scientific notation and rounding to one number after the decimal: a. You want to convert 8.56 m into μm (show the detail of the calculation)
8.56 m x 10
6
μm/m = 8.56 x 10
6
μm = 8.6 x 10
6
μm
b. You want to convert 4654 mg into g (show the detail of the calculation) 4654 mg x 10
-3
g/mg = 4.654 g = 4.7 g c. How many grams are in 0.052 kg? (show the detail of the calculation) 0.052 kg x 10
3
g/kg = 52 g = 5.2 x 10
1
g d.
How many cm are in 3,907 μm? (show the detail of the calculation) 3,907 μm x10
-4
cm/ μm = 0.3907 cm = 3.9 x 10
-1
cm e.
You and your lab partner are looking at a specimen under the microscope. Your lab partner calculated that the size of this specimen is 7.6 X 10
7
nm. Given the large size of the specimen you realize that nm are not an appropriate unit to use. Convert the size to a more appropriate unit. nm = 10
-9
m ; cm = 10
-2
m ; therefore 1 nm = 10
-9
m x 10
2
cm/m = 10
-7
cm 7.6 x 10
7
nm x 10
-7
cm/nm = 7.6 cm
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