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The length limit on Enotes responses prevents all 30 of your questions from being fully answered. In the future please cluster your questions according to format or subject matter, so that they will be easier to respond to, and so that problems may be more easily addressed; for example, in Section 4: Accuracy and Precision, you did not include a picture that is necessary to answer question 3, and there are no instructions on what is to be done with the four questions.

3. Conversions

1. mg to kg

There are various ways of expressing the relationship between exponential factors; the simplest depiction here is to use grams. Grams are the “standard” upon which these measurements are based. A milligram is one-thousandth of a gram, and a kilogram is one thousand grams. Thus, 1000x1000 = 1 million milligrams would fit into a kilogram.

The easiest way to set up conversions is to write what you have, including units. Then, on the right side of this amount, write the conversion factor (the statement which relates the unit you have to the unit you want). 1 million mg = 1 kg is our conversion factor. Now orient the conversion factor so that the unit you already have is on the bottom; this way, the units will cancel out, leaving you with units of what you wanted to convert to.

46,756,790mg x (1kg/1,000,000mg) = 46.756790kg

2. hours to seconds.

The conversion factor is based on 60 seconds in a minute, and 60 seconds in an hour.

1 hour = 3600 seconds.

5.6 hours x (3600 seconds / 1 hour) = 20,160 seconds

3. cm to inches

The conversion here can be looked up from reference; 1cm = 0.3937 inches

13.5cm x (.3937 inches / 1cm) = 5.315 inches

4. C to F

This is more of a math equation than a conversion factor. To convert Celsius to Fahrenheit, multiply the Celsius temperature by (9/5) and add 32.

47 x (9/5) + 32 = 116.6 F

5. Significant Digits

General rules for sigfigs:

-Nonzero numbers always count.

-Zeros between nonzeros count

-Any zero at the end of a number (trailing) zeros count only if there is a decimal.

-Zeros at the beginning of a number never count

1. 3. Trailing nonzeros without a decimal do not count.

2. 2. Leading zeros do not count.

3. 8. All nonzeros count.

4. 4. Trailing zeros with a decimal count.

5. 8. Zeros between nonzeros count.

6. 7.

7. 2.

8. 8.

**Scientific Notation**

The rules for scientific notation are;

-The expression must be in the form of (number) times (ten to a power)

-The initial number must be a single-digit integer

-The integer must be followed by a decimal if there is more than one significant figure in the original number

-Any additional significant digits appear after the decimal

To find the appropriate power of ten:

If the number is greater than zero, count from the decimal place (or the “ones”-value digit) up to the first number.

If the number is less than zero, count the places between the decimal place and the first number, plus the initial zero.

- 7 x 10e10
- 4.8 x 10e-8
- 6.789 x 10e7
- 7.05 x 10e4
- 4.509008 x 10e8
- 9.045 x 10e-3
- 2.3 x 10e-2