Question

1. what is $6.37 \times 10^2$ in standard form?

a. 0.00637
b. 0.0637
c. 637
d. 63700

1. which is the best example of a number written in scientific notation?

a. $0.5 \times 10^5$
b. 0.1254
c. $5.367 \times 10^{-3}$
d. $12.5 \times 10^2$

1. the length of the amazon river in south america is 6,400 kilometers. what is the length written in scientific notation?

a. $6.4 \times 10^2$
b. $6.4 \times 10^3$
c. $6.4 \times 10^4$
d. $6.4 \times 10^5$

1. a virus is viewed under the microscope. its diameter is 0.0000002 meters. how would this length be expressed in scientific notation?

a. $2 \times 10^{-7}$
b. $2 \times 10^{-6}$
c. $2 \times 10^6$
d. $2 \times 10^7$

1. the value of $25^\circ$c is a measurement of

a. density
b. temperature
c. mass
d. volume

1. the amount of space occupied by a substance is its ______.

a. mass
b. density
c. weight
d. volume

Explanation:

Question 1

Step1: Recall scientific notation to standard form

To convert \(6.37\times10^{2}\) to standard form, we know that \(10^{2}=100\).

Step2: Multiply 6.37 by 100

\(6.37\times100 = 637\).

Step1: Recall scientific notation rules

Scientific notation is in the form \(a\times10^{n}\) where \(1\leq|a|\lt10\) and \(n\) is an integer.

Step2: Check each option

• Option a: \(0.5\times10^{5}\), \(a = 0.5\) which is less than 1, not in scientific notation.
• Option b: \(0.1254\) is not in scientific notation form.
• Option c: \(5.367\times10^{-3}\), \(1\leq5.367\lt10\) and \(n=- 3\) (integer), so it is in scientific notation.
• Option d: \(12.5\times10^{2}\), \(a = 12.5\) which is greater than 10, not in scientific notation.

Step1: Recall scientific notation conversion

To convert 6400 to scientific notation, we need to write it as \(a\times10^{n}\) where \(1\leq|a|\lt10\).

Step2: Determine \(a\) and \(n\)

6400 can be written as \(6.4\times1000\), and \(1000 = 10^{3}\), so \(6400=6.4\times10^{3}\).

Answer:

c. 637

Question 2