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Scientists Create New Material Five Times Lighter and Four Times Stronger Than Steel
(scitechdaily.com)
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"one fifth the mass" is not the same thing as "five times lighter"
Consider something that weighs half as much. It's 50% lighter ... 0.5 times lighter. Something that weighs 0.2 times as much has 20% of the weight, and is 80% lighter. If it weighed 1% as much, it would be 99% lighter (0.99 times lighter). If it was 100% lighter ... it would weigh nothing. Five times lighter would be -4 times the original mass.
We already have accurate and precise ways to describe less mass (albeit leaving aside for the moment the distinction between mass and weight). It's no harder to say "one fifth" than "five times", but only one is correctly describing what is going on.
You're right that we have precise ways to say this, but people like seeing bigger numbers rather than smaller ones, and most people aren't "precise" about anything.
It's a relative metric, not an absolute one. And since they're using the word "lighter" (i.e. less massive) it means that they're talking about the reciprocal of mass.
I.e. 1/5 the mass = 5 times "lighter"
If something is 50% the mass of something else, you could say the the heavier one is twice as heavy as the light one. Which means that the light one is two times "lighter" than the heavy one.
But I agree with your sentiment, relative comparisons of reciprocals is confusing at the best of times.
It's not the word "lighter" that's the issue, it's the word "less". If I say something weighs 80% less, ... you know how much that is. 100% less, it weighs even less -- nothing at all. 500% less (i.e. 5 times less), suddenly it weighs more?