There are three key ways to round numbers:(i) (ii) (iii)
to the nearest 10, 100, 1000, etc;
to a certain variety of significant figures;
to a certain number of decimal places.

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Note that a measured length such as "12 centimeter to the nearest cm" way that the actual size lies in between 11.5 cm and also 12.5 cm.

By convention, we normally round 0.5 approximately the next totality number, for this reason in fact,

11.5 cm ≤ actual size 9

where the dot above the 9 way that that is repetitive indefinitely, or recurs.

It is necessary to view that 12.49 is not the top bound, as, for example, the length could have to be 12.498.


Example 1

A football enhance is watched by 56 742 people. Create this number correct to the nearest,


(a)(b)(c)
10 000,
60 000
1000,
57 000
10.
56 740

Example 2

Write every of the adhering to numbers exactly to 3 significant figures:


(a)(b)(c)(d)
47 316
47 300
303 971
304 000
20.453
20.5
0.004368
0.00437

Example 3

Write every of the adhering to numbers exactly to the number of decimal areas stated:


(a)(b)(c)(d)
0.3741 to 2 d.p.
0.37
3.8451 come 2 d.p.
3.85
142.8315 to 1 d.p.
142.8
0.000851 to 4 d.p.
0.0009

Example 4

State the upper and also lower bounds for each that the complying with quantities and write an inequality because that the actual value in every case.


(a)

4 mm come the nearest mm.


Upper tied = 4.5 mmLower bound = 3.5 mm

3.5 mm ≤ really value reduced bound = 14.5 kg

14.5 kg ≤ really value reduced bound = 4.555 mm

4.555 m ≤ really value inquiry 1

Round every of the following numbers to the nearest 100:


(a)(b)(c)(d)
the nearest million,
the nearest 10,
the nearest 1000,
the nearest 100.


Question 3

Write every of the adhering to numbers exactly to 3 far-reaching figures:


(a)(b)(c)(d)(e)(f)
7.431
8.269
4.7135
11.925
24.8603
44.0019


Question 5

Write each of the adhering to numbers exactly to the number of far-ranging figures stated:



Question 7

Barry ring the number 374.49 come 375.



Is Barry correct?

- choose -CorrectIncorrect



Give the exactly answer to the nearest whole number.



Question 8

Use a calculator to carry out the following calculations. In each case, offer the answer exactly to 2 far-ranging figures.



Question 9

The mass of a ship is declared as 47 384 tonnes come the nearest tonne. Space the following statements correct?






(a)(b)(c)
the nearest 100 grams, grams
the nearest 10 grams, grams
the nearest kg. kg



Viv"s best throw was measured together 35.42 m.Could Viv"s throw actually have actually been much more than 35.42 m ?

- YesNo




(i)


(ii)

Which 2 rivers have the same length come the nearest 100 km?

and also


(i)

Write the length of each river rounded to the nearest 10 km.

RiverLength in kilometres tothe nearest kmLength in km to thenearest 10 km
Severn354
Thames346
Trent297
Wye215
Dee113


(ii)


150 kilometres ≤ river length km and km.


250 km ≤ river length 245 kilometres ≤ river length Question 13


*

The size of one envelope is 21 cm to the nearest cm.

What is the smallest possible real length of the envelope?

cm

(b)

The expression on the number line listed below shows every the possible real lengths the the envelope.

Write down the correct numbers because that the lower and upper borders of the interval, represented on the diagram by A and B.


*

(c)
*

The length of a map is 20.5 centimeter to the nearest tenth of a cm.

See more: Weight Of A 20 Dollar Bill S Weigh? Money Weight Calculator

The expression on the number line below shows all the possible real lengths of the card.