Chapter 2.2, Problem 15PP

Interpretation Introduction

(a)

Interpretation:

The given equation needs to be expressed in scientific notation.

$(4\times {10}^2)\times (1\times {10}^8)$

Concept introduction:

The form of expressing too big or too small numbers into a convenient decimal form is known as Scientific notation.

Answer to Problem 15PP

$(4\times {10}^2)\times (1\times {10}^8)=(4\times 1)\times {10}^{2+8}=4\times {10}^{10}$

Explanation of Solution

Any number can be expressed as number between 1 and 10 that is coefficient and this coefficient is multiplied by 10 raised to the power of the exponent. This whole notation is known as Scientific notation.

Scientific notation for the multiplication is: $(4\times {10}^2)\times (1\times {10}^8)=(4\times 1)\times {10}^{2+8}=4\times {10}^{10}$

(b)

Interpretation Introduction

Interpretation:

The given equation needs to be expressed in scientific notation.

$(2\times {10}^4)\times (3\times {10}^2)$

Concept introduction:

The form of expressing too big or too small numbers into a convenient decimal form is known as Scientific notation.

Answer to Problem 15PP

$(2\times {10}^4)\times (3\times {10}^2)=(2\times 3)\times {10}^{-4+2}=6\times {10}^{-2}$

Explanation of Solution

Any number can be expressed as number between 1 and 10 that is coefficient and this coefficient is multiplied by 10 raised to the power of the exponent. This whole notation is known as Scientific notation.

Scientific notation for the multiplication is: $(2\times {10}^4)\times (3\times {10}^2)=(2\times 3)\times {10}^{-4+2}=6\times {10}^{-2}$

(c)

Interpretation Introduction

Interpretation:

The given equation needs to be expressed in scientific notation.

$(6\times {10}^2)÷(2\times {10}^1)$

Concept introduction:

The form of expressing too big or too small numbers into a convenient decimal form is known as Scientific notation.

Answer to Problem 15PP

$(6\times {10}^2)÷(2\times {10}^1)=(6÷2)\times {10}^{2-1}=3\times {10}^1$

Explanation of Solution

Any number can be expressed as number between 1 and 10 that is coefficient and this coefficient is multiplied by 10 raised to the power of the exponent. This whole notation is known as Scientific notation.

Scientific notation for the division is: $(6\times {10}^2)÷(2\times {10}^1)=(6÷2)\times {10}^{2-1}=3\times {10}^1$

(d)

Interpretation Introduction

Interpretation:

The given equation needs to be expressed in scientific notation.

$(8\times {10}^4)÷(4\times {10}^1)$

Concept introduction:

The form of expressing too big or too small numbers into a convenient decimal form is known as Scientific notation.

Answer to Problem 15PP

$(8\times {10}^4)÷(4\times {10}^1)=(8÷4)\times {10}^{4-1}=2\times {10}^3$

Explanation of Solution

Any number can be expressed as number between 1 and 10 that is coefficient and this coefficient is multiplied by 10 raised to the power of the exponent. This whole notation is known as Scientific notation.

Scientific notation for the given division is: $(8\times {10}^4)÷(4\times {10}^1)=(8÷4)\times {10}^{4-1}=2\times {10}^3$