1.4.1 Scientific (Exponential) Notation

Question 1

Scientific (Exponential) Notation

Answer 1

• Scientific notation is an efficient means of expressing extremely large and small numbers.
• To add numbers in scientific notation, they must both be expressed to the same power of ten.
• To multiply or divide numbers in scientific notation, consider the number and power parts separately.
• For powers and roots of numbers in scientific notation, consider the number and power parts separately

Question 2

Avogadro’s number

Answer 2

• Scientific notation is an efficient means of expressing
  extremely large and small numbers.
• In scientific notation, numbers are expressed in the form r x 10^t, where r is a number greater than or equal to one and less than ten and t is an integer. For example,
  Avogadro’s number can be expressed in scientific notation as 6.022 x 10^23.
• From the decimal representation, if the decimal point is
  moved to the left, t is a positive integer. If the decimal point is moved to the right, t is a negative exponent.

Question 3

note

Answer 3

• To add numbers in scientific notation, they must both be expressed to the same power of ten. For example, to add 3.94 and 6.7 x 10^–1, express both to the same power of ten.
• Once both numbers are expressed to the same power of ten, simply add them together. If the result is no longer in proper scientific notation, the decimal place might have to be moved to the left or right and the power of ten adjusted accordingly.
• To multiply or divide numbers in scientific notation, consider the number and power parts separately.
• For example, to multiply 3.94 x 10^2 by 6.7 x 10^–3, multiply 3.94 by 6.7, and add the exponents together.
• Similarly, to divide 3.94 x 10^2 by 6.7 x 10^–3, divide 3.94 by 6.7, and subtract the second exponent from the first. This yields 0.59 x 10^5, or 5.9 x 10^4 in proper scientific notation.
• For powers and roots of numbers in scientific notation,
  consider the number and power parts separately.
• To raise a number in scientific notation (r x 10^t) to the power b, raise r to the b and multiply t times b.
• Similarly, to take the bth root of a number in scientific
  notation (r x 10^t), take the bth root of r and divide t by b.

Question 4

How many significant figures are in the number 53,630,208?

Answer 4

• 8

Question 5

answer

Answer 5

• 3.0 × 10^2

Question 6

Select the choice that correctly shows the product of

110^a)(2^10^b

Answer 6

• (1*2) * 10^(a+b)

Question 7

Calculate the following and express the answer in scientific notation with the proper number of significant figures.
(5907) × (10000)

Answer 7

• 5.907 × 10^7

Question 8

Which of the following choices shows the number 0.00504 written in scientific notation?

Answer 8

• 5.04 × 10^−3

Question 9

Which of these numbers is properly written in scientific notation and has the least value?

Answer 9

• 6.833 × 10−2

Question 10

What is the correct sum for the expression 2.78 × 10^2 + 3.5 × 10^3, written in scientific notation using the correct number of significant figures?

Answer 10

• 3.8 × 10^3

Question 11

Which of the following shows 10,000 in scientific notation with three significant figures?

Answer 11

• 1.00 × 10^4

Question 12

Which of the following numbers in scientific notation has the greatest value?

Answer 12

• 2.53 × 10^4

Question 13

answer

Answer 13

• 8.0 × 10^−2