[rounding to decimal places ][ rounding to tens, hundreds etc. ]

[ rounding to significant figures ][ estimates ][ bounds ]

__Rounding to a required number of decimal places__

The key is to look at the number after the required number of decimal places.

e.g. write 7.718__ 6__ to 3 decimal places(d.p.)

The __ 6__ is what is called the '

If this number is '5' or more, then the 3rd decimal is '__rounded up__'. Less than '5' and the decimal stays the same.

In this example 5.7186 becomes 5.719

The '8' is rounded up to '9', because '6' is 5 or more.

__Examples__

19.17 to 1 d.p. is 19.2

0.0214 to 2 d.p. is 0.02

34.4255 to 3 d.p. is 34.426

__Rounding to tens, hundreds, thousands etc. __

__examples__

24,214 to the nearest thousand is 24,000

24,214 to the nearest hundred is 24,200

35,712 to the nearest thousand is 36,000

35,712 to the nearest hundred is 35700

795 to the nearest hundred is 800

56 to the nearrest ten is 60

__Rounding to a number of significant figures__

The required number is found by ignoring any zeros infront or behind the line of numerals and rounding where needed.

__Example #1 __

0.001292 ................to 3 significant figures

the three figures are 1 2 9

__answer = 0.00129__

__Example #2 __

120,101 ................to 4 significant figures

the four figures are 1201

__answer = 120,100__

__Example #3 __

13.27 ................to 3 significant figures

the 13.272 rounds up to 13.3

the three figures are 133

__answer = 13.3 __

__Estimates__ - An estimate is a rough approximation, usually of a calculation.

The rule is to round to __ one__ significant figure.

__Example #1 __

__Example #2__

__Example #3__

__Upper & lower Bounds __

The use of 'bounds' is a practical mathematical method quite different from 'decimal rounding'. Do not confuse the two. Decimal rounding depends on a '5 or more' being rounded up. Bounds is quite different.

Whenever measurements are expressed in the real world they are often given an upper bound(highest value) and a lower bound(lower value).

__example __ - A length of wood is 1500 mm long, correct to the nearest 'm.m.'.

The upper bound is therefore: 1500.5 m.m.

The lower bound is therefore: 1499.5 m.m.

__Note __- The upper & lower bounds are HALF the degree of accuracy.

In our example, m.m., that is half of 1 m.m.

__Example #1__ - A poster measures 99.5 cm x 192.2 cm correct to the nearest 0.1 cm.

Find the upper and lower bounds for the poster's dimensions, hence find its maximum & minimum area.( to 2 d.p.)

upper bounds 99.55 , and 192.25................lower bounds 99.45 , 192.15

maximum area = 99.55 x 192.25 = 19138.488 = __19138.49 (2d.p.) sq. c.m. __

minimum area = 99.45 x 192.15 = 19109.318 = __19109.32 (2 d.p.)sq. c.m.__

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__Example #2__ - A rocket travels a vertical distance of 50k.m.(correct to nearest k.m.) in 23.1 seconds(correct to the nearest 0.1 second.

What are the upper and lower limits to the rocket's average speed?

upper bounds 50.5k.m. , and 23.15 sec...........lower bounds 49.5k.m. , 23.05

The highest average speed is with the largest distance divided by the smallest time.

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