Answered

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Estimate the product of 0. 235 and 13. 467 to the nearest hundredth.

Sagot :

sqdancefan

Answer:

  3.16

Step-by-step explanation:

An estimate is usually made to 1 or 2 significant digits. Here, we want an estimate accurate to hundredths, which will be 3 significant digits.

Estimate

We can round the numbers to some reasonable values, then look at the effect of the rounding error.

  0.235 × 13.467 = (0.25 -0.015) × (13.5 -0.033)

  = 0.25(13.5) -0.25(0.033) -0.015(13.5) +0.015(0.033)

  = 3.375 -0.00825 -0.2025 + (something small)

  ≈ 3.375 -0.008 -0.203 = 3.375 -0.211 = 3.164

  0.235 × 13.467 ≈ 3.16

Mental math

Note that the values we have can make use of mental math methods.

  0.25 = 1/4 = (1/2)(1/2)

  0.015 = 0.01(1 +1/2)

That is, dividing numbers by 2 mentally is usually not terribly difficult. (Here, it is made more difficult by the odd digits involved.)

  0.25 × 13.5 = (1/2)(13.5/2) = 1/2(6.75) = 3.375

  0.015 × 13.5 = 0.135 +0.135/2 = 0.135 +0.0675 = 0.2025

or, recognizing that 1.35 = 1.5 -.15, ...

  0.015 × 13.5 = (0.01)(1.5) × (10)(1.5-.15) = 1.5²×(.1 -.01) = .225 -.0225

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Additional comment

A calculator gives the actual product as 3.164745, so our estimate is accurate to hundredths.

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