Drill Questions: Magnitudes

At any point, you can submit your answers by collecting them and uploading them to the class site.

No answers yet collected

Link to upload site

If requested by your instructor, please identify here the people from whom you received assistance on this assignment.

If the answers that have been loaded automatically are not yours, press this button before starting your work:
What is the order of magnitude of 56000? d04-1
2.5       3.5       4.5       5.5       6      

What is the order of magnitude of -900000000.0? d04-2
7       8.5       9       9.5       10.5      

What is the order of magnitude of 17? d04-3
-0.5       0.5       1       1.5       2.5      

What is the order of magnitude of -0.00043498? d04-4
-5.5       -5       -4       -3.5       -2.5      

What is the order of magnitude of 7.4? d04-5
-1       0       1       1.5       3      

What is the order of magnitude of -0.00000064? d04-6
-8       -7.5       -6       -5       -4.5      

.

Drill 4. 1 Usually you read the order of magnitude from the integer following the e. For instance, the order of magnitude of 1.56e13 is simply thirteen. But for the devious purposes of this drill problem, we’ve written some of the numbers in non-standard form.

The standard form for writing a number in scientific notation has, as you know, two components: a mantissa and an exponent. The mantissa is written to have one non-zero digit to the left of the decimal point. The exponent must always be an integer, that is \(\ldots, -2, -1, 0, 1, 2, 3, \ldots\).

  1. Which one of the following is not in standard form?
ptb-1-o3f
0.2e-6       1.56e4       -9.2e-2       4.5e17      

  1. Which one of the following is not in standard form?
ptb-2-fdw
7.1e2       7.4e-1       7e2.1       7.9e0      

Suppose you have a number written in non-standard form, e.g. 36.525e1. To change this to standard form, you need to divide the mantissa by 10, that is, move the decimal point one place to the left. To compensate for the division by 10, you need to raise the exponent by 1. This gives 3.6525e2

Similarly, when the leading digit of the mantissa is zero, for instance 0.0052e1 conversion to standard form requires moving the decimal point to the right until the leading digit is non-zero. To compensate for moving the decimal point, you need to subtract the number of places moved from the exponent. So to put 0.0052e1 in standard form we need to move the decimal point three places to the right and, in compensation, subtract 3 from the exponent. This gives 5.2e-2.

  1. For each of these mantissas, how do you have to move the decimal point to place the mantissa in a standard form for scientific notation? (3L means “three places to the left” while 2R means two places to the right.)

3a. 92425.01

ptb-3a-clse
4L       3L       2L       1L       OK as is       1R       2R       3R       4R      

3b. 0.00314e3

ptb-3b-s3d
4L       3L       2L       1L       OK as is       1R       2R       3R       4R      

3c. 1.00026e-3

ptb-3c-s3d
4L       3L       2L       1L       OK as is       1R       2R       3R       4R      

  1. Three of the following numbers have the same order of magnitude. Which one doesn’t?
ptb-4-dkwd
65e5       7.229e6       659e7       0.0063e9      

Drill 4. 2  

  1. Which kind of scale is this?   sca-1-iynwq
    linear     or       magnitude      
  1. Which kind of scale is this?   sca-2-btuqn
    linear     or       magnitude      
  1. Which kind of scale is this?   sca-3-ujkzw
    linear     or       magnitude      
  1. Which kind of scale is this?   sca-4-xgjzi
    linear     or       magnitude      
  1. Which kind of scale is this?   sca-5-jtbam
    linear     or       magnitude      
  1. Which kind of scale is this?   sca-6-rozql
    linear     or       magnitude      
  1. Which kind of scale is this?   sca-7-byroe
    linear     or       magnitude      

Drill 4. 3 In everyday speech, a “decade” corresponds to 10 years, “two decades” to 20 years, and so on. In magnitude graphics, a decade refers to something different. On a magnitude scale, as on all numerical scales, there is a lowest marked value and a higher marked value. If the higher marked value is 10-times the size of the lowest, that scale covers one decade. If the higher marked value is 100-times the size of the lowest—that is, two orders of magnitude bigger—the scale is said to cover two decades. A span of three orders of magnitude corresponds to three decades, and so on.

  1. How many decades are spanned by this interval: [0.01 to 10]?
psp-1-3kdw
0       1       2       3       4       5       6      

  1. How many decades are spanned by the interval [10 to 1000]?
psp-2-ired
0       1       2       3       4       5       6      

  1. How many decades are spanned by the interval [0.3 to 30]?
psp-3-yseld
0       1       2       3       4       5       6      

Sometimes an interval doesn’t cover a full order of magnitude. For instance, the in scale [10 to 30], the higher value is not even 10 times the lower. But, when the higher number is 3 times the lower, we way that the interval covers “half a decade.” Why “half?” Two half orders of magnitude places the higher value at \(3 \times 3 \approx 10\) times the lower value. Since since a factor of 10 is one decade, a factor of 3 is (roughly) half a decade.

  1. How many decades are spaned by the interval [10-300]?
psp-5-2ess
0.5       1       1.5       2       2.5      

  1. How many decades are covered by this scale?

psp-5-nkvd
3.5       4       4.5       5       5.5       6      

  1. How many decades are covered by this scale?

psp-6-gru
0.5       1       1.5       2       2.5