Question

Amanda says that a human fingernails has a thickness of about 4.2 x 10^-4 meter. Justin says that a human fingernails has a thickness of about 0.42 millimeters .

What is the width in meters written in standard notation?


Do Justin’s and Amanda’s measurements agree? Explain .

Explain why Justin’s estimate of the thickness of a human fingernail is made appropriate than Amanda’s estimate.

Answer 1

See below

Explanation:

1. Standard notation

4.2 × 10⁻⁴ m

A negative exponent indicates

• A number between 0 and 1.
• That the decimal point is shifted that number of places to the left.

4.2 × 10⁻⁴ tells you that the decimal number is 4.2, with the decimal point moved four places to the left.

The number becomes 0.000 42 .

2. Metres to millimetres

`4.2 * 10^(-4)\text{ m} * \frac{10^(3)\text{ mm}}{\text{1 m}} = 4.2* 10^(-1)\text{ mm = 0.42 mm}}`

3. Measurements agree?

Yes, because both measurements are the same as 0.42 m.

4. More appropriate measurement

Most measurements should be expressed as a number between 0.1 and 1000, because most people aren’t particularly good at visualizing larger or smaller numbers.

Justin's measurement of 0.42 mm is more appropriate than Amanda's measurement of 4.2 × 10⁻⁴ m.