Chapter MH, Problem 2PP

Solution

(a)

Interpretation: The given operation needs to be performed.

  $\left(5.0\times {10}^6\right)+\left(3.0\times {10}^7\right)$

Concept Introduction: To perform this type of operation, the exponent form must be common for both scientific forms. The numbers with the same exponent form can be added or subtracted normally.

  $3.5\times {10}^7$

The given expression is as follows:

  $\left(5.0\times {10}^6\right)+\left(3.0\times {10}^7\right)$

This can be rewritten as follows:

  $\left(0.5\times {10}^7\right)+\left(3.0\times {10}^7\right)$

Taking ${10}^7$ common.

  $\left(0.5+3.0\right)\times {10}^7$

Or,

  $3.5\times {10}^7$

(b)

Interpretation: The given operation needs to be performed.

  $\left(1.8\times {10}^9\right)+\left(2.0\times {10}^8\right)$

Concept Introduction: To perform this type of operation, the exponent form must be common for both scientific forms. The numbers with the same exponent form can be added or subtracted normally.

  $2.0\times {10}^9$

The given expression is as follows:

  $\left(1.8\times {10}^9\right)+\left(2.0\times {10}^8\right)$

This can be rewritten as follows:

  $\left(1.8\times {10}^9\right)+\left(0.2\times {10}^9\right)$

Taking ${10}^9$ common.

  $\left(1.8+0.2\right)\times {10}^9$

Or,

  $2.0\times {10}^9$

(c)

Interpretation: The given operation needs to be performed.

  $\left(3.89\times {10}^{12}\right)-\left(1.9\times {10}^{11}\right)$

Concept Introduction: To perform this type of operation, the exponent form must be common for both scientific forms. The numbers with the same exponent form can be added or subtracted normally.

  $3.7\times {10}^{12}$

The given expression is as follows:

  $\left(3.89\times {10}^{12}\right)-\left(1.9\times {10}^{11}\right)$

This can be rewritten as follows:

  $\left(3.89\times {10}^{12}\right)-\left(0.19\times {10}^{12}\right)$

Taking ${10}^{12}$ common.

  $\left(3.89-0.19\right)\times {10}^{12}$

Or,

  $3.7\times {10}^{12}$

(d)

Interpretation: The given operation needs to be performed.

  $\left(6.0\times {10}^{-8}\right)-\left(4.0\times {10}^{-9}\right)$

Concept Introduction: To perform this type of operation, the exponent form must be common for both scientific forms. The numbers with the same exponent form can be added or subtracted normally.

  $5.6\times {10}^{-8}$

The given expression is as follows:

  $\left(6.0\times {10}^{-8}\right)-\left(4.0\times {10}^{-9}\right)$

This can be rewritten as follows:

  $\left(6.0\times {10}^{-8}\right)-\left(0.4\times {10}^{-8}\right)$

Taking ${10}^{-8}$ common.

  $\left(6.0-0.4\right)\times {10}^{-8}$

Or,

  $5.6\times {10}^{-8}$