Question

The average distance from the sun to the planet Mercury is about 58,000,000 km. The diameter of a human hair is about 0.0025 cm.

What is the distance from the sun to Mercury written in scientific notation?

What is the diameter of a human hair written in scientific notation?

In comparing the measurements in Parts (a) and (b), what else must be done before a comparison is made?

What is the comparison? Show which distance, in scientific notation, is larger using inequality symbols. (ex. 2>1 or 3.1< 2.567)

Answer 1

a) 58,000,000 km = 5.8 x 10^7 km

b) 0.0025 cm = 2.5 x 10^ -3 cm

c) Before a comparison is made we need to convert one of units of measurement. (cm to km OR km to cm)

Answer 2

Distance of Sun and Mercury = 58,000,000 km.
In Scientific notation, it would be: 5.8 × 10⁷ Km

Diameter of a human hair = 0.0025 cm
In scientific notation, it would be: 2.5 × 10⁻³ cm

Before Comparison, we need to bring cms to Kms or vice-versa, so we can easily calculate then, here, we will go from cm to Km.
2.5 × 10⁻³ × 10⁻⁵ Km = 2.5 × 10⁻⁸

Now, we can compare the values,
5.8 × 10⁷ Km > 2.5 × 10⁻⁸

[ reason. - power of smaller number is in negative, it means, it is denominator, which would be very small as compared to other ]

Hope this helps!