Question

in exercises 1 - 2, choose the number that is written in scientific notation.

1. t·y 34.5×10^5 m·e 3.45×10^6 y·p 0.345×10^7
2. b·g 0.77×10^(-3) i·r 7.7 + 10^(-4) s·l 7.7×10^(-4)

in exercises 3 - 6, find the value of n.
in exercises 19 - 22, write the number in scientific notation.

1. 22.2×10^3 p·o 2.22×10^5 1·t 2.22×10^7
2. 0.222×10^8 t·f 2.22×10^4 c·s 2.22×10^9
3. 0.54×10^(-4) g·l 5.4×10^(-6) u·p 5.4×10^(-16)
4. 54×10^(-15) q·h 5.4×10^(-14) x·v 5.4×10^(-5)

a b c d e f g h i j k l m n o p q r s t u v w x y z
exponents and exponential functions: scientific notation
punchline • algebra • book b
©2006 marcy mathworks

Explanation:

Step1: Recall scientific - notation rules

Scientific notation is of the form $a\times10^{n}$, where $1\leq|a|\lt10$ and $n$ is an integer.

Step2: Analyze Exercises 1 - 2

Exercise 1:

• For $34.5\times10^{5}$, $a = 34.5\geq10$, not in scientific - notation.
• For $3.45\times10^{6}$, it is in scientific - notation as $1\leq3.45\lt10$.
• For $0.345\times10^{7}$, $a = 0.345\lt1$, not in scientific - notation.

Exercise 2:

• For $0.77\times10^{-3}$, $a = 0.77\lt1$, not in scientific - notation.
• For $7.7 + 10^{-4}$, this is not in the form $a\times10^{n}$, not scientific - notation.
• For $7.7\times10^{-4}$, it is in scientific - notation as $1\leq7.7\lt10$.

Step3: Analyze Exercises 19 - 22

Exercise 19:

Given $22.2\times10^{3}$, rewrite it as $2.22\times10^{4}$ (not among the options). But if we rewrite $22.2\times10^{3}=2.22\times10^{1 + 3}=2.22\times10^{4}$. The correct scientific - notation equivalent among options for a related manipulation is $2.22\times10^{5}$ which is wrong for $22.2\times10^{3}$, but if we consider moving the decimal one more place in the wrong way.

Exercise 20:

Given $0.222\times10^{8}$, rewrite it as $2.22\times10^{7}$ (not among the options).

Exercise 21:

Given $0.54\times10^{-4}$, rewrite it as $5.4\times10^{-5}$ (not among the options). But $0.54\times10^{-4}=5.4\times10^{-1}\times10^{-4}=5.4\times10^{-5}$. The closest correct - like form among options is $5.4\times10^{-6}$ which is wrong.

Exercise 22:

Given $54\times10^{-15}$, rewrite it as $5.4\times10^{-14}$ since $54\times10^{-15}=5.4\times10^{1}\times10^{-15}=5.4\times10^{-14}$.

Answer:

1. m·E. $3.45\times10^{6}$
2. s·L. $7.7\times10^{-4}$
3. None of the given options are correct for $22.2\times10^{3}$
4. None of the given options are correct for $0.222\times10^{8}$
5. None of the given options are correct for $0.54\times10^{-4}$
6. q·H. $5.4\times10^{-14}$