NOTES 4 Calculations Using
Scientific and Standard Notation
with Units and Sig. Figs.
Name______________________________
Date__________
Block_____
Use your reference sheets for sig. figs.
Refer to the handout on Measurement for the powers of 10 review.
On your calculator: learn to use the “EE” or “SCI” or “EXP” button for scientific notation.
Do NOT use the “^” key for scientific notation.
Remember, your calculator uses the rules of mathematical operations. (In order: parentheses,
exponents, multiplication, division, addition, and subtraction.) Therefore, you must key in
parentheses, etc., so that the calculator will compute the correct answer.
General rule for “when do I use scientific notation?” : use scientific notation for all
numbers having the largest place value in the ten thousands value or greater and for all
decimal numbers having the first sig. fig. in the one ten-thousandth place. See below for
examples:
No scientific notation needed
all numbers up to and including 9 999 ( 4 578; 44.790)
decimals: wherever a decimal answer is written with no more than 3 decimal places
(0.100; 0.010; 0.001; 0.120; 0.099; 0.999; 0.125)
NOTE: all decimal numbers are written with a “zero” before the decimal!
Scientific notation is needed for
numbers greater than 9 999 (24 001 = 2.400 1 x 104; 570 000 000 = 5.7 x 108)
decimals that have the first sig. fig. in the 4th decimal place or beyond
(0.00050 = 5.0 x 10-4; 0.000 000 247 = 2.47 x 10-7)
NOTE: any units are written AFTER the entire number: 5.02 x 106 mg; 3.4 x 10 –5 kg
REMEMBER: in scientific notation:
a) the number BEFORE the decimal cannot be greater than 9 or less than 1;
b) the only numbers written before the “times” sign are the significant numbers.
Calculate the following, and write your answer in scientific notation and in the appropriate
number of s.f.! Pay attention to the units! (m x m = m2, etc.!)
1.
(2.58 x 10 5 m) ( 1.35 x 10 15 m ) = _______________________________
2.
(6.003 x 10 – 12 km) ( 3.0 x 10 – 9 km) = ____________________________
3.
(9.0 x 10 23 mm) ( 5.000 x 10 – 16 mm) = ____________________________
4.
5.
6.
(2.58 x 10 5 m2)
( 1.35 x 10 15 m)
= ______________________
(6.003 x 10 – 12 cm3) = _____________________
( 3.0 x 10 – 9 cm2)
(9.0 x 10 23 mm2)
( 5.000 x 10 – 16 mm)
= _______________________
Calculate the following, write your answer first unrounded in standard notation and then
rounded to the appropriate number of sig. figs. in scientific notation: (an example is given)
50 m x 3 m = 150 m2 = 2 x 102 m2
7.
388 m x 4.0 m = ______________ ___ _
= ______________________________
8.
65 mm x 1996 mm = ______________________ = _________________________
9.
0.004 m x 0.24 m = ____________________ = _____________________________
10.
454 m x 0.006 m = ______________________ = ___________________________
11.
8 255 cm x 0.077 cm = _______________________ = _________________________
12. 0.0148 m x 6 973 m = ______________________ = __________________________
Calculate the following; where possible, cancel units:
13. (43.54 m)(75.87 m)(31.2 m) =
(9.0 m)(0.02 m)
14. 3094.82 m + 7957.03 m + 30.0035 m = __________________________
15. 4.84 x 1031 km + 6.23 x 1033 km = ____________________________
16. (1.045 x 1014 m)(5.5020 x 109 m) = ____________________________
17. (2.68 x 10 25 cm2)(8.421 x 10 –4 cm) =
(7.60 x 10 –5 cm)(1.0 x 10 –24 cm)
18. (783 mmHg)(254 K)(23.52 L) =
(752 mmHg) (273 K)
__________________________ __
19. (575.3 g) x (23.75 oC) x (4.186 J) =
(g)(oC)
20.
(1.045 x 1014 m) – (5.5020 x 1017 m) = ____________________________
21.
(2.088 x 1023 m) – (3.75 x 1025 m) = ___________
22.
(105 m x 10 –14 m) = ______________________________
23.
(108 mm x
24.
(104 cm3) (107 cm2) = _____________________________
(101 cm) (106 cm3)
25.
1013 mm) = ______________________________
0.35 g Ba x 1 mole Ba_ x 6.02 x 1023 atoms =
137.3 g Ba
1 mole