A perimeter and exponentiation problem

Question

A wheel of a car lasts for 5000 scandinavian miles, and then it needs to be switched. The diameter of the car's wheel is 70 centimetres. How many laps has the wheel spinned before it needs to get changed? Answer with an exponent.

First off, I just want to say that 1 scandinavian mile = 10 kilometres = 10000 metres if anyone was wondering. I know that I need to divide the length that the wheel can drive with the perimeter of the wheel but I don't know how to do it with exponents.

My book says that the answer is 2.3*10^7 laps.

I'm sorry if I've written this a bit messy, my keyboard isn't functioning correctly.

Answer 1

Based on the answer, when your book said "answer with an exponent" what it meant was, "give the answer in scientific notation to two significant figures."

$5000$ scandinavian miles is $5000*10000*100=5000000000=5*10^9$ centimeters ($10000$ meters in a scandinavian mile, $100$ centimeters in a meter). The circumference of the wheel is $\pi d=70\pi$ centimeters. Dividing $5*10^9$ centimeters by $70\pi$ centimeters (note that units must be consistent) gives $22736420.4417...$ which is approximately equal to $23000000$ which, in scientific notation, is $2.3*10^7$.

Answer 2

First you have to calculate the perimeter of the wheel. The perimeter of a circle (wheel) is $2\Pi r$.

The diameter of the wheel is $2r=70\text{cm}$. Thus the perimeter of the wheel is $70\text{cm}\cdot \Pi$

Now you can transform $50,000=5\cdot 10^4$ km in cm. Here you have to multiply it by $100,000=10^5$ (A factor of 1,000 to get the metres and a factor of 100 to get the cm). This gives $5\cdot 10^9\text{cm}=500\cdot 10^7\text{cm}$.

To get the answer, you have divide the driven distance of $500\cdot 10^7\text{cm}$ by the perimeter of the wheel $70 \cdot \Pi \ \text{cm}$

$\Pi=3.14159...$