State the number of significant figures, scientific notation, and unit prefix. 1

Question

State the number of significant figures, scientific notation, and unit prefix. 1760 (). () (K) 0,00126 (). () (m) 288,000 (). () (M) 8.4700 (). () (d) 0.01750 (). () (c) Perform the following operations the correct number of 35.42 times 22.3 = () 6.5/9.330 = () 2.865 + 8.2 + 24.32 = () 845 - 12 1 - 8.332 = () Three students named Abe, Bob, and Carl make measurements of the length of table using a meter stick. Each student's measurements are tabulated in the following table. Modem laser technique made a value of 3.475 m in this measurement. Find the percent error of Bob Find the percent difference between and Abe and Bob Find the uncertainty of measurement of Carl Find the measurement of Bob. Make a graph of Length vs Trials for three students (Spread Sheet like MS Excel).

Explanation / Answer

1.)   Five rules govern significant figures:

1. Non-zero digits are always significant; 1.121 has four significant digits.

2. Any zeros between two significant digits are significant; 1.08701 has six significant digits.

3. Zeros before the decimal point are placeholders and not significant; in the number .00254, only the 2,5 and 4 are significant, meaning the number has 3 significant figures.

4. Zeros after the decimal point and after figures are significant; in the number 0.2540, the 2, 4, 5 and last 0 are significant.

5. Exponential digits in scientific notation are not significant; 1.12x106 has three significant digits, 1, 1, and 2.

Scientific Notation To express very large or very small numbers, scientists express values in terms of "a x 10b ", where “a” is a number between 1 and 10 and “b” is number of places the decimal place had to move in order to express “a” as a number between 1 and 10. This type of expression is called scientific notation. 1 = 1x100 10 = 1x101 100 = 1x102 1000 = 1x103 etc.. The value in the exponent place describes how many zeroes there are in the number being represented. The number 100 has 2 zeroes; it's scientific notation is 1X102 .

Some Unit prefixes.

Femto f 10-15 1 femtoliter (fL)= 0.000000000000001

pico p 10-12 1 picoliter, (pL) = 0.000000000001 l

nano n 10-9 1 nanogram, (ng) = 0.0000000001 g

etc..

a.) (4),(1.760*10^1),(0.01760K)

b.) (3),(1.26*10^-3),(126m)

c.) Sorry this was a bit unclear i'll solve assuming the figure to be 288,000

(6),(2.88000*10^5),(0.288000M)

d.) (5),(8.4700*10^0),(0.84700d)

e.) (4),(1.750*10^-2),(1.750c)

2.) Addition and Subtraction of Significant Figures Addition and subtraction of significant figures follows a simple rule: The final value must have only as many decimals as the original value with the least number of decimal places.

Significant Figures in Multiplication and Division The rule governing multiplication and division of significant figures is slightly different than that for addition and subtraction, but just as simple: The final value can only have as many significant figures as the original value with the least significant figures.

a.) 789

b.) 0.69

c.) 35.3

d.) -11.9

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