5 More Tips for Understanding Weights and Measures

A few weeks ago, I realized that I have pretty much zero intuition about how much a gram weighs. I know—kind of tragic, right?

Nope, not tragic at all. In fact, I see it as an opportunity, because whenever I stumble upon something like this that I don't know, I'm a fan of figuring it out.

So, if you're at all like me and are not exactly sure just how heavy grams, ounces, pounds, stones, and tons are, then you're in luck! Because that's exactly what we'll be talking about today.

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Tip 1: Grams and Paper Clips

Let's kick things off by clearing up my, perhaps your, and certainly everybody else's uncertainty about exactly how much 1 gram weighs. As we've learned in a discussion of mass versus weight, I've actually confused the issue a bit in the previous sentence by proclaiming the gram to be a measure of weight—of course, it's more properly dubbed a measure of mass. So, with that in mind, how much mass is 1 gram?

1 gram is about the mass of a metal paperclip.

The quick and dirty comparison to keep in your head is that 1 gram is about the mass of a metal paperclip. Or, if you prefer, it's about the mass of a US dollar bill. As these comparisons show, 1 gram isn't much mass at all—at least by everyday standards. Although if you're a proton, you'd actually think that 1 gram is a huge mass, since a proton's mass is only about 1 trillion trillionth of a gram.

The gram is the fundamental unit of mass in the metric system, but you'll often hear masses measured in kilograms, too. A kilogram is simply 1,000 grams, which turns out to be pretty close to the mass of a pair of soccer balls.

Tip 2: Ounces and Pencils

As you'll remember from last week's show about the units we use to measure volume, the word "ounce" can refer to either a volume or a mass measurement. As we learned, the volumey kind of ounce is actually called the "fluid ounce," so there really isn't all that much cause for confusion.

As we also learned, the quick and dirty way to think about ounces is to know that a pencil and an empty soda can each weigh about 0.5 oz., and a tennis ball weighs about 2 oz. If you want a more direct comparison, a slice of normal sandwich bread has a mass of roughly 1 ounce.

Ounces are the primary unit of mass used in the U.S. and a few other parts of the world—i.e., everywhere that isn't metric. If you're wondering how an ounce compares to a gram, it turns out that 1 ounce is a lot more mass than 1 gram. In fact, 1 ounce is approximately equal to 28.35 grams.

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Tip 3: Pounds and Soccer Balls

The weight of a standard sized soccer ball or football is approximately 1 pound.

For one reason or another, most of us have learned at some point that 16 ounces is equal to what's called 1 pound—the favorite unit (in the U.S., at least) for measuring the mass of dogs, cats, fruit, humans, and pretty much everything else.

The quick and dirty method for intuiting 1 pound of weight (or mass) is to know that the weight of a standard sized soccer ball or football (either kind) is approximately equal to 1 pound.

A few fun facts about the pound:

• The pound is abbreviated "lb," a seemingly odd choice until you find out that the pound evolved from the ancient Roman unit of weight called the libra—hence the abbreviation.
• Way, way back in the day, the monetary unit known as the British pound was actually related to the unit of weight of the same name. Once upon a time, a British pound was equal to the value of a pound of silver. Needless to say, this relationship no longer holds.

Tip 4: Stones and Bags of Sugar

Folks in the U.S. tend to measure their weight (or mass) in pounds, but people in Britain tend to use a unit called the stone. A stone is simply equal to 14 pounds, so a person who weighs 170 pounds equivalently weighs a little over 12 stone.

My favorite quick and dirty way to think intuitively about weights in the 10-20 pound range—and thus, in the 1 stone range—is in terms of bags of sugar. Yes, you read that right: bags of sugar. Most standard-sized bags of sugar sold in the U.S. weigh 5 pounds, which means that my beloved 1 stone cat weighs a little less than 3 bags of sugar.

A Boeing 747 weighs about 370 tons.

Tip 5: Tons, Dairy Cows, and 747s

Let's wrap things up by stepping way up the mass scale to talk about the unit known as the ton. This is one of those units which has a technical meaning, but has also made its way into colloquial usage. When something is extremely heavy, we often say it "weighs a ton."

But if we're being more precise about things, how much does that ton actually weigh? That depends on what kind of ton we're talking about.

The regular, old-fashioned ton is equal to 2,000 pounds. The metric ton, on the other hand, is equal to 1,000 kg—which turns out to be about 2,205 pounds. Either way, a ton is a ton of mass. If you'd like some quick and dirty ways to think about just how much mass this is, typical dairy cows (which, if you've ever been right next to one, you know are huge) weigh about a ton, while small cars weigh about two tons, a blue whale weighs about 200 tons, and a Boeing 747 weighs about 370 tons.

Wrap Up

OK, that's all the weights and measures we have time for today.

Please be sure to check out my book, The Math Dude’s Quick and Dirty Guide to Algebra. And remember to become a fan of The Math Dude on Facebook, where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

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