Video: Converting a Measure of Length between Unfamiliar Units

An orgyia, an ancient Greek measure of length, is approximately equal to 72.78 inches. It’s also equivalent to 6 smaller Greek units called podes. Based on these relationships, 69 Greek podes is equivalent to how many feet, to the nearest tenth? Remember: 12 inches = 1 foot.

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Video Transcript

An orgyia, an ancient Greek measure of length, is approximately equal to 72.78 inches. It’s also equivalent to six smaller Greek units called podes. Based on these relationships, 69 Greek podes is equivalent to how many feet to the nearest tenth? Remember, 12 inches equals one foot.

Well, we’ve been given quite a lot of information here, so the first thing to do is to summarise what we know. Firstly, one orgyia is roughly equal to 72.78 inches. And an orgyia is also equal to six podes. But we also know that 12 inches is equal to one foot. Now, we’ve got to express 69 Greek podes in feet. Now, we need to plan a method.

Well, we know the relationship between podes and orgyia, so we can convert podes into orgyia. And we also approximately know the relationship between orgyia and inches, so we can convert those orgyia into inches. Once we know the distance in inches, we can use the fact that we know that 12 inches equals a foot to convert it into feet.

If we visualise this, the distance one orgyia is the same distance as six podes. If I take the number of orgyia and multiply it by six, I’ll get the number of podes. For example, a distance of two orgyia is six times two. That’s 12 podes. And going in the other direction, if I’ve got a distance in podes, if I divide the number of podes by six, it will tell me the number of orgyia. The number of orgyia is always as sixth as many as the number of podes.

So, if we started off with 69 podes, there would be 69 divided by six orgyia. So at this stage, I’m not going to attempt to simplify that number. I’m just gonna leave it as 69 over six. So, we’ve completed stage one. We’ve converted 69 podes into the number of orgyia.

Now stage two, converting orgyia to inches. If one orgyia is approximately 72.79 inches, then I need to multiply that number of orgyia by 72.78 to get the number of inches. And if I knew the number of inches, I could divide that by 72.78 to get the number of orgyia. But in step two, I’m converting orgyia to inches, so I need to multiply the number of orgyia by 72.78. So, in step two, we take the number of orgyia, 69 over six, and we multiply that by 72.78 to get the number of inches.

Now, in step three, we’ve gotta convert inches into feet. Well, one foot is 12 inches. So, if I know the number of feet and I multiply that by 12, that tells me the number of inches. But we know the number of inches, and we want to convert that into feet. So, there’s gonna be as twelfth as many feet as there are inches. I’ve got to divide the number of inches by 12. So, to complete step three, I take the number of inches, 69 over six times 72.78, and divide that by 12 to get the number of feet. And when I tap that into my calculator, I find that 69 podes is approximately equal to 69.7475 feet.

And now, all that remains is me to round that to the nearest tenth. Well, this digit here is in the tenths column, so I’m going to need one decimal place. If I cover up all the digits to the right of that seven, I can see that I got 69 and seven-tenths. But I need to slide back that cover a little bit and do a sneaky peek in the hundredths column to see whether that seven can stay as a seven or whether it needs to be rounded up to an eight.

If that digit in the next column is less than five, then we know that this number is nearer to 69.7 than 69.8. If that digit was five or more, then we would be closer to 69.8 than 69.7. So, we’d have to round up. In this case, it’s four, which is less than five. So, we can slide back the cover and leave our number as 69.7. And our answer is 69 podes is equal to 69.7 feet to the nearest tenth.

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