Download scientific (exponential) notation

1.2
SIGNIFICANT DIGITS / SIGNIFICANT FIGURES
Accuracy –
Precision –
The precision of any measurement depends upon the precision of the instrument used. The digits in an answer which imply more
accuracy or precision than the measurements justify are not significant and should dropped so that those digits which remain truly
imply the precision of the original measurements. The remaining digits are called significant digits or significant figures.
Significant digits or significant figures consist of :
A QUANTITY contains both a _____________________ and a ______________________.
Measured numbers Exact numbers Determining which zeros are significant -- because zeros must be written both as placeholders and as indicators of the precision of
the measurement, we must learn how to distinguish between them. The following rules are used to determine the number of significant
digits:
1.
2.
3.
4.
5.
All non-zero numbers are significant
Sandwich zeroes are significant
Leading zeroes are NEVER significant.
Trailing zeroes are significant if decimal point is present.
Exact numbers have as many significant figures as needed.
Rules for Rounding:
1. If the eliminated digit is less than 5, leave alone.
2. If the eliminated digit is 5 or greater, round up.
In Class Practice:
Determine the number of significant digits in each of the following:
1.
0.02
________
11.
142
________
2.
0.020
________
12.
0.073
________
3.
501
________
13.
1.071
________
4.
501.0
________
14.
10810
________
5.
5000
________
15.
5.00
________
6.
5000.
________
16.
55.320
________
7.
6051.00 ________
17.
1.010
________
8.
0.0005 ________
18.
154
________
9.
0.1020 ________
19.
8710
________
10001
20.
1.0004
________
10.
________
Round each of the following to three significant digits.
1.
88.473
____________
9. 69.95
____________
2.
8505
____________
10. 0.000056794
____________
3.
976450
____________
11. 67.048
____________
4.
699.5
____________
12. 3.002
____________
5.
123.98
____________
13. 0.0300
____________
1.2
6.
0.00086321
____________
14. 90100
____________
7.
12.17
____________
15. 54.009
____________
8.
8040
____________
SCIENTIFIC (EXPONENTIAL) NOTATION
Putting Ordinary Numbers into Scientific Notation:
Scientists (and those studying science) frequently must deal with numbers that are very_______________ or very _______________.
Have you met Avogadro's number (6.02 x 10 23)?
Or have you calculated the wavelength of red light (6.10 x 10-7 m)?
If those numbers weren't written the way they are, all of us who must deal with them would be spending much of our time just counting the zeros that
separate the figures from the decimal point. To avoid that kind of time wasting, a method of writing very large and very small numbers was invented.
The rules for writing numbers in scientific notation are
1. The first figure is a number from 1 to less than 10.
2. The first figure is followed by a decimal point and then the rest of the figures.
3. Then multiply by the appropriate power of 10.
In class practice: Write each of these numbers in scientific notation:
17 =
____________________
0.000000614 =
____________________
3=
____________________
0.0037004 =
____________________
5.000 =
____________________
0.00000038 =
____________________
215 =
____________________
0.01010 =
____________________
7,000,631 =
____________________
0.00000000001 =
____________________
Putting Scientific Notation into Ordinary Numbers:
If the number ends with a positive exponent, move the decimal point to the right. If the number ends with a negative exponent, move
the decimal point to the left.
In class practice:
Write each of the following as ordinary numbers.
2.926847212 x 109 =
6
___________________
4.000 x 10-2 =
-5
___________________
4.29 x 10 =
___________________
4.92x10 =
___________________
3.286 x 104 =
___________________
8.429 x 10-1 =
___________________
2
5.92000 x 10 =
3
4.37521 x 10 =
___________________
___________________
-2
___________________
-4
___________________
5.376 x 10 =
2.986 x 10 =
3.
1.2
Significant Figures and Scientific Notation – HW 1
I. Give the number of significant figures in each.
1.
967
6.
2.700
11.
0.0076009
2.
967,000
7.
304
12.
670,000
3.
9.67
8.
9.
13.
0.00872
4.
0.00967
9.
90
14.
8.53x103
5.
4050
10.
7.805
II. Round each of the following to four significant figures.
15.
2.16347x105 ______________
17.
7.2513
_____________
16.
4.000574x105 ____________
18.
375.6523
____________
III. Round each of the following to two significant figures.
19.
3.512
____________
21.
2.751x108
____________
20.
25.631
____________
22.
3.9814 x105
____________
IV. Round each of the following to the nearest whole number.
23.
56.912
____________
25.
0.5182
____________
24.
3.4125
____________
26.
112.511
____________
V. Round each of the following to the nearest hundredth.
27.
54.7421
____________
29.
79.2588
____________
28.
100.0925
____________
30.
0.9114
____________
VI. Express each of the following numbers in scientific notation. (Remember to pay attention to zeros. include them if they are
significant, do not include them If they are not)
31.
325
________________
36.
0.361
_________________
32.
70
__________________
37.
0.0428
___________________
33.
96,400
__________________
38.
0.00573
_________________
34.
5,921
__________________
39.
0.0005438
35.
6,587,324,000 ________________
40.
0.00005673 _________________
___________________
VII. Write each of the following as ordinary numbers. (Watch for significant zeroes)
41.
3.64 x104
46.
2.97 x10-4
__________________
42.
3.9734 x105 ._________________
47.
3.88 x10-2
_________________
43.
6.285x103 _________________
48.
5.65 x10-1___________________
44.
6.7978x100 _________________
49.
3.7283 x 10-4 _________________
45.
5.8643 x102 _________________
50.
4.763x10-3 __________________
_________________