Scientific notation and significant figures

Light travels at $300\,000\,000\ \text{m/s}$. Write this speed in standard form.

A red blood cell has a diameter of about $0,000008\ \text{m}$. Express this length in standard form.

One day has $86\,400$ seconds. Write it in standard form.

Write the number $4,5\cdot10^{3}$ using all its digits.

Of these three ways of writing the same number, only one is in correct standard form. State which one it is and explain what is wrong with the other two:

1. a) $25\cdot10^{4}$
2. b) $2,5\cdot10^{5}$
3. c) $0,25\cdot10^{6}$

Fill in the blanks: $6\,000 = 6\cdot10^{\dots}$ and $0,003 = 3\cdot10^{\dots}$.

Order these numbers written in standard form from smallest to largest: $3,2\cdot10^{4}$; $9,8\cdot10^{3}$; $1,5\cdot10^{5}$; $4\cdot10^{4}$. Explain what you look at first to compare them: the leading digits or the exponents.

How many times larger is $6\cdot10^{8}$ than $2\cdot10^{5}$? Do this by dividing the powers of ten and give the result in standard form.

Calculate $(3\cdot10^{4})\cdot(2\cdot10^{3})$ and express the result in standard form.

How many significant figures does each of these measurements have? Explain the criterion you followed in each case.

1. a) $2,50\ \text{cm}$
2. b) $0,034\ \text{kg}$
3. c) $1,02\ \text{L}$

Using the ruler in your pencil case, you measure the thickness of a coin and get $0,2\ \text{cm}$. a) How many significant figures does this measurement have? b) Why does it not make sense to write $0,2000\ \text{cm}$ if the ruler only marks millimetres?

Ximena calculates the density of a stone and the calculator shows $2,68473\ \text{g/cm}^3$. The balance she used measured to three significant figures, and the measuring cylinder to only two. a) Knowing that a result cannot be more precise than the least precise value, to how many significant figures should Ximena give her result? b) Write it correctly rounded.