ESTIMATION OR APPROXIMATION

HELLO, WELCOME BACK TO CLASS

 

An estimate is an answer to a problem that is close to the solution, but not necessarily exact. Estimating can come in handy in a variety of situations, such as buying a computer. You may have to purchase numerous devices: a computer tower and keyboard for $1,295, a monitor for $679, the printer for $486, the warranty for $196, and software for $374. Estimating can help you know about how much you’ll spend without actually adding those numbers exactly.

Estimation usually requires rounding. When you round a number, you find a new number that’s close to the original one. A rounded number uses zeros for some of the place values. If you round to the nearest ten, you will have a zero in the ones place. If you round to the nearest hundred, you will have zeros in the ones and tens places.

Because these place values are zero, adding or subtracting is easier, so you can find an estimate to an exact answer quickly.

It is often helpful to estimate answers before calculating them. Then if your answer is not close to your estimate, you know something in your problem-solving process is wrong

Note: Any number greater than or equal to five (5) is regarded as one (1) and any number less or equal to four (4) is regarded as zero (0)

Rounding up of numbers (10, 100, 1000)

  • Nearest ten (10)
  • Nearest hundred (100)
  • Nearest thousand (1000)
  1. eg round up 2756 to nearest 10, 100, 1000

2756 = 2760 to the nearest 10

275 6= 2800 to the nearest 100

2 7 5 6 = 3000 to the nearest 1000

  1. eg convert 1427 to the nearest 10, 100, 1000

142 7 = 1430 to the nearest 10

14 2 7 = 1400 to the nearest 100

1 4 2 7= 1000 to the nearest 1000

Decimal places

This has to do with counting of numbers after the point

E.g.  0.2= 1dp

  1. 3 = 1dp

2.65 = 2dp

315.18= 2dp

0.124 = 3dp

1.419 = 3dp

E.g.  Convert 0.4579 to 1, 2 and 3 decimal places

  1. 4 579 =  0.5 = 1dp

0.4 5 79 = 0.46 = 2dp

  1. 4 5 7 9 = 0. 458 = 3dp

Significant figure

Note: Any zero (0) before any number, cannot be considered significant

E.g.               0.001 = 1 significant figure

0.07 = 1 significant figure

1.1 = 2 significant figures

13 = 2 significant figures

  • = 2 significant figures

0.0143 = 3 significant figures

14.7 = 3 significant figures

  1. 09 = 3 significant figures

0.008 = 1 significant figure

E.g.  Convert 0.4186 to 1, 2 and 3 significant figures

0.4186 = 0.4 to 1 significant figure

0.4186 = 0.42 to 2 significant figures

0.4186 = 0.419 to 3 significant figures

E.g. convert 1.0519 to 1, 2 and significant figures

1.0519 = 1                         1 significant figures

1.0519=1.1                        2 significant figures

1.0519=1.05                      3 significant figures

 

Quiz

  1. Approximate 6784 to the nearest hundred.
  2. Convert 1.6518 to 1, 2 significant figure.
  3. Convert 0.4579 to 1, 2 and 3 decimal places
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