D.J. wants to estimate the quotient of 373 ÷ 5. He chooses the estimate 500 ÷ 5

400 ÷ 5 = 80370 ÷ 5 = 74

Step-by-step explanation:

A closer estimate would be to round to the nearest hundred. 500 is really far way from 373, so it probably won't give a very accurate estimateAnother closer estimate would be to round to the nearest tens. By rounding here, you are guaranteed a very close estimate to the real answer. The real answer is 74.6 and if we round to the nearest tens, the answer is 74. These two answers are only 0.6 away from each other, so this is a very, very accurate estimate.

I hope this helps!

9514 1404 393

exact: 1.3924×10^-10rounded to 2 sf: 1.4×10^-10

Step-by-step explanation:

The factor 10^-6 can be brought out:

  ((5.5 +6.3)×10^-6)^2 = (11.8^2)×10^-12 = 1.3924×10^-10

Often, a problem like this wants you to round to a precision appropriate to the given values. Here, that is 2 significant figures:

  ≈ 1.4×10^-10

Additional comment

Your scientific or graphing calculator can do this nicely, even showing you the result in scientific notation. A spreadsheet can do the same.

The usual rules of exponents apply.

  (a^b)(a^c) = a^(b+c)

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)