Question

A certain insect is approximately 4 × 10^-2 inches long. A second insect is about 1.3 × 10^-1 inches long. What is the total length of the two insects in inches

Answer 1

• 1.7 × 10^-1 inches

Given :

• Length of 1st insect : 4 × 10^-2 inches
• Length of 2nd insect : 1.3 × 10^-1 inches

Task :

• To find the total length of the two insects in inches.

Solution :

In order to find the total length of the given two insects, we'll add both of their length by converting both the power of 10 same and then adding the numbers.

• 
  `\rightarrow \: 4 × 10^(-2) in \: + 1.3 × 10^(-1) in`
• 
  `\rightarrow \: 4 × 10^(-2) in \: + 13 × 10^(-2) in`
• 
  `\rightarrow \:( 4 + 13)× 10^(-2) in \:`
• 
  `\rightarrow \: 17 × 10^(-2) in`
• 
  `\rightarrow \: 1.7 * 10 {}^( - 1) in`

Thus, the total length of the given two insects would be 1.7 × 10^-1 inches .

Answer 2

(1.7 × 10⁻¹) inches = 0.17 inches

Explanation:

To determine the total length of the two insects, we simply add the length of each insect:

`\textsf{Total length}=\left(4 * 10^(-2)\right)+\left(1.3 * 10^(-1)\right)`

The length of each insect is given in scientific notation. To add two terms in scientific notation we need to make the exponents the same.

Express the length of the first insect so that the exponent of 10 is -1. To do this, divide the number 4 by 10 and multiply 10⁻² by 10. In other words, move the decimal point one place to the left and add 1 to the exponent:

`\begin{aligned}4 * 10^(-2)&=(4)/(10) * 10^(-2)* 10^1\\\\&=0.4 * 10^(-2+1)\\\\&=0.4 * 10^(-1)\end{aligned}`

Therefore:

`\textsf{Total length}=\left(0.4 * 10^(-1)\right)+\left(1.3 * 10^(-1)\right)`

Factor out the common term 10⁻¹:

`\textsf{Total length}=\left(0.4 +1.3\right) * 10^(-1)`

Add the numbers:

`\textsf{Total length}=1.7 * 10^(-1)`

Therefore, the total length of the two insects in scientific notation is (1.7 × 10⁻¹) inches.

To convert this into a decimal:

`\begin{aligned}1.7 * 10^(-1)&=(1.7)/(10) * 10^(-1)* 10^1\\\\&=0.17* 10^(-1+1)\\\\&=0.17 * 10^(0)\\\\&=0.17 * 1\\\\&=0.17\;\sf inches\end{aligned}`