# If a 10K race is 10.0 kilometers (1.00 x 10^4 meters), what is the distance in yards? (Given: 1...

## Question:

If a 10K race is 10.0 kilometers (1.00 {eq}\times {/eq} 10{eq}^4 {/eq} meters), what is the distance in yards? (Given: 1 meter = 1.09 yards)

## Units:

Most quantities in science have units appended to them. Units help us identify what quantity we are looking at. For instance, we know that time is measured in seconds while lengths are measured in meters. There are also different units of measurement in a single quantity to make visualizing the quantity more easy. For instance, we already know how long an hour is, but intuitively we don't think about how long 3,600 seconds are.

## Answer and Explanation:

Given:

- {eq}\displaystyle x = 10,000\ m {/eq} is the length

To convert the distance to yards, we will have to cancel out the meter unit. So in one meter there are 1.09 yards. We can thus do the conversion as:

{eq}\displaystyle x = 10,000\ m \left(\frac{1.09\ yd}{1\ m} \right) {/eq}

We cancel the meter unit:

{eq}\displaystyle x = 10,000\ \require{cancel}\cancel{m} \left(\frac{1.09\ yd}{1\ \require{cancel}\cancel{m}} \right) {/eq}

So essentially, we will be multiplying the numbers and appending the *yd* unit. We thus get:

{eq}\displaystyle \boxed{x = 10,900\ yd} {/eq}

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