A Stitch in Haste

Remember scientific notation? Writing, for example, “9,000” as 9 x 10³? It makes manipulation of large numbers and the equations that use them much simpler, since you just have to play with coefficients and exponents. Neat-o.

Unless you’re talking about the federal budget:

House and Senate Republican leaders have reached tentative agreement on a budget that envisions $10 billion in Medicaid savings over the next five years and at least $70 billion in tax cuts, congressional officials said Thursday.
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These officials, who spoke on condition of anonymity, said the tentative agreement envisions spending of about $2.6 trillion for the fiscal year that begins Oct. 1.
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Overall, officials said the agreement envisioned savings of roughly $35 billion over five years from federal benefit programs.
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Overall, the spending plan envisions about $106 billion in tax cuts, officials said, about $70 billion of which can be protected against a filibuster.
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Much of the controversy had surrounded Medicaid. The House initially voted to trim up to $20 billion from anticipated Medicaid spending. In the Senate, though, [Republican] Sen. Gordon Smith...led a successful effort to strip out all the savings from the health care program. In negotiations that involved the White House, Republican leaders in the two houses eventually closed in on a compromise of $10 billion.

A reduction in Medicaid increases (not a cut in spending, mind you, but a reduction in planned increases) of $10 billion over five years. Still don’t need scientific notation for that – it’s $2 billion per year. The total spending cuts non-increases of $35 billion over five years mean $7 billion per year.

Now let’s jump into scientific notation: $2 billion is $2 x 10⁹; $7 billion is $7 x 10⁹.

The total federal budget is projected to be $2.6 trillion in fiscal year 2005. That’s $2.6 x 10¹².

Here’s where the real joy of scientific notation comes in: to express the reductions non-increases in percentage terms, all we need do is subtract the exponents: 9-12 = -3. So easy!

Cleaning up the arithmetic, 7/2.6 x 10^-3 = 2.7 x 10^-3, or in everyday terms 0.27% of the federal budget.

I forgot to mention: scientific notation is also useful for dealing with very small numbers, like this puny, barely symbolic dent in the federal budget. Very very big budget numbers, and very very small changes in those very very big numbers. Such are the joys sorrows of scientific notation.

Republican House, Republican Senate, oh and Republican White House. And what do we have to show for it? A 0.27% reduction non-increase in the budget.

Remind me again why there’s a libertarian wing of this party?

POST SCRIPT: Here's another analysis where scientific notation would have come in handy.