Colin DonnellyMCAT Physics and Math 10.1: Arithmetic and Significant Figures
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Scientific notation
Scientific notation is a method of writing numbers that takes advantage of powers of ten. In scientific notation, a number is written with a significand and an exponent.
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The first part of scientific notation is called the _____. (three answers)
significand, coefficient, or mantissa
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The second part of scientific notation is called the _____.
exponent
(technically, if "102" is the second part, then only "2" is the exponent)
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The range of the absolute value of the significand is _____.
[1,10)
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The exponent in scientific notation can be _____.
any whole number
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Significant figures
Significant figures (also known as the significant digits, precision or resolution) of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something.
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Significant figures are determined by the _____.
precision of the instrument being used for measurement
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If the width of an object is stated to be 55.2 mm after being measured with a ruler, what are the smallest markings on the ruler?
tenths of a mm (i.e. the 0.2 is an estimate)
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When presented with data, look for accuracy of the measurements in two ways: identifying the number of _____, and looking for _____.
significant digits in a number
error margins or statistical significance
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If the width of an object is stated to be 55.2 mm after being measured with a ruler, what are considered to be significant digits?
50, 5, and 0.2
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731,000
Which digits are significant?
731,000
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69.420
Which digits are significant?
69.420
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The significant figures of a measurement are ...
... all of the values that are known for certain, and (possibly) the first uncertain, or estimated, digit.
This really depends on who you ask. Kaplan says that the estimate is not significant, while others say that it is significant.
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0.00700
Which digits are significant?
0.00700
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Leading zeroes (significant?)
Any zeroes to the left of the first nonzero digit are considered leading zeroes and are not significant.
0.00700
First three zeroes are leading zeroes
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45,670
Which digits are significant?
45,670
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45,670.0
Which digits are significant?
45,670.0
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731,0Ō0
Which digits are significant?
731,000
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An overline is used to indicate _____.
the last significant digit
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If there are zeroes to the right of the last nonzero digit and _____, then those zeroes are significant figures. If there is _____, they are not significant.
there is a decimal point in the number
no decimal point
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Are trailing zeroes significant?
Maybe
If there is a decimal, then they are significant..
If there is an overline, then only the zeroes up to the zero with an overline are significant.
If there is no decimal and no overline, then they are not significant.
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When multiplying and dividing numbers, the number of significant figures of the answer is equal to _____.
the least number of significant figures of the initial numbers
For example:
700. (3 sig figs) * 0.20 (2 sig figs) = 140 (2 sig figs), not 140.
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900.
Which digits are significant?
900.
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When adding and subtracting numbers, ...
... keep track of decimal points, not significant figures. The answer may only have as many decimal points as the initial number with the fewest decimal diigts.
For example: 0.6000 (4 decimal points) - 0.004 (3 decimal points) = 0.596 (3 decimal points) not 0.6 (1 sig fig)
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Even if answer choices are close, it is generally acceptable to round to _____.
one decimal place
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When rounding numbers to be multiplied, round one number up and one number _____.
down to compensate
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When rounding numbers to be divided, round _____.
both numbers in the same direction to compensate
