A tear in an aircraft hull has a length of 1.4x10-4 inch. The tear becomes 1000 times longer. What is the new length of he tear write your answer in scientific notation

The answer is 1.4×10⁻¹ inch

Step-by-step explanation:

Scientific notation is a way of writing very large or very small numbers.

Now the steps to solving this problems are as follows:

1. Length of hull = 1.4×10⁻⁴.

2 Multiplication factor = 1000, which is 10×10×10 and which can also be written as 10³ (which is read 10 to the power of 3), because 10 multiplies itself 3 times to give 1000.

Next, the question said the tear becomes 1000 times longer, which means that the original tear is multiplied by 1000 hence:

1.4×10⁻⁴ multilied by 1000 or 1.4×10⁻⁴ multiplied by 10³

= 1.4×10⁻⁴×10³.

To solve this easily I have to introduce an exponential law. and it states:

mᵃ × mᵇ = mᵃmᵇ = mᵃ⁺ᵇ. The law states that when two exponents are multiplied, the result is the same as adding the sum of their powers.

In our example; 1.4×10⁻⁴×10³, we can group the expression into like terms as follows; 1.4×(10⁻⁴×10³), then we can apply the law to the expression in bracket.

so showing just the expression in the bracket:

10⁻⁴×10³ = 10⁽⁻⁴⁺³⁾ = 10⁻¹.

putting this back into the original expression:

1.4×10⁻⁴×10³ = 1.4×10⁽⁻⁴⁺³⁾  = 1.4×10⁻¹ (in scientific notation).

you should also note that 10⁻¹ here is the same as . So, if were not writing it in scientific notation is will be written as 1.4 × = 0.14.