Scientists often have to deal with numbers that are either very large or very small. For example, the radius of the Sun is approximately 696,000 kilometers, while bacterial cells are as small as 1.9 × 10-4 millimeters. Express each number in an alternate form.In expanded notation, each bacterial cell is ___________
millimeters wide?

Answer:

• The scientific notation for 696,000 km is 6.96 × 10⁵ km

• The expanded notation for 1.9 × 10⁻⁴ mm is 0.00019 mm

Explanation:

The notation used by scientists to represent either very large of very small numbers is called scientific notation.

Scientific notation represents the number  using powers of ten. The general form for a number expressed in scientific notation is:

Where:

• m can be either positive or negative and its absolute value must be greater than or equal to zero and less than 10: 0 ≤ | m |  < 10.

• p can be any integer number (either positive or negative).

For the given example of the radius of the Sun, the scientific notation representation of 696,000 km is:

• 6.96 × 10⁵ km : since the number 696,000 should be divided by 100,000 to obtain the number 6.96, you must multiply the latter by 100,000 which is 10⁵.

For the bacterial cell, the number 1.9 × 10⁻⁴ mm needs to be changed to expanded notation. The negative 4 power means that you must divide 1.9 by 10,000 which is the same that moving the decimal point 4 places to the left. That is:

• 1.9 × 10⁻⁴ mm = 0.00019 mm

Answer:

Each bacterial cell is (1\times 0.0001+ 9\times 0.00001) millimeters wide.

Explanation:

The radius of the Sun is approximately 696,000 kilometers

We are given:

Radius of the Sun = 696,000 km  (standard notation)

Converting this into scientific notation, we get:

 (Scientific notation)

Size of bacterial cell = millimeters (Scientific notation)

Converting this into standard notation, we get:

 (Standard notation)

0.00019 mm in expanded notation:

0.00019 mm = (1\times 0.0001+ 9\times 0.00001) mm

Each bacterial cell is (1\times 0.0001+ 9\times 0.00001) millimeters wide.