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3.3 Rounding
3.3 Rounding
You know how to round decimal numbers to one or two decimal places (d.p.). The ‘degree of
accuracy’ is the number
You can use exactly the same method to round decimal numbers to of decimal places you
more than two decimal places. are working to.
t -PPL BU UIF EJHJU JO UIF QPTJUJPO PG UIF degree of accuracy.
t *G UIF WBMVF PG UIF OVNFSBM UP UIF SJHIU PG UIJT EJHJU JT PS NPSF JODSFBTF UIF EJHJU CZ
If the value is less than 5, leave the digit as it is.
Worked example 3.3a
Round the number 5.376 398 to the given degree of accuracy.
a one decimal place b three decimal places c fi ve decimal places
a 5.376 398 = 5.4 (1 d.p.) The digit in the fi rst decimal place is 3. The digit to the right of it is 7.
7 is more than 5, so round the 3 up to 4. The letters ‘d.p.’ stand for
‘decimal place’.
b 5.376 398 = 5.376 (3 d.p.) The digit in the third decimal place is 6. The digit to the right of it is 3.
3 is less than 5 so the 6 stays the same.
c 5.376 398 = 5.376 40 (5 d.p.) The digit in the fi fth decimal place is 9. The digit to the right of it is 8.
8 is more than 5 so round the 9 up to 10. This has the effect of rounding
the fourth and fi fth digits (39) up to 40. Notice that you must write down
the zero at the end, as the number must have fi ve decimal places.
You also need to know how to round numbers to a given number of signifi cant fi gures.
!e %rst signi%cant %gure in a number is the %rst non-zero digit in the number.
For example: 4 is the %rst signi%cant %gure in the number 450
8 is the %rst signi%cant %gure in the number 0.008 402.
To round a number to a given number of signi%cant %gures follow exactly the method above.
t -PPL BU UIF EJHJU JO UIF QPTJUJPO PG UIF EFHSFF PG BDDVSBDZ
t *G UIF OVNCFS UP UIF SJHIU PG UIJT EJHJU JT PS NPSF JODSFBTF UIF EJHJU CZ
If the number is less than 5, leave the digit as it is.
Worked example 3.3b
a Round 4286 to one signifi cant fi gure.
b Round 0.080 69 to three signifi cant fi gures.
a 4286 = 4000 (1 s.f.) The fi rst signifi cant fi gure is 4. The digit to the right of it is 2.
2 is less than 5, so 4 stays the same. Replace the 2, the 8 and the
6 with zeros to keep the size of the number consistent. In this case,
rounding to one signifi cant fi gure is the same as rounding to the nearest
1000. The letters ‘s.f.’ stand for ‘signifi cant fi gure’.
b 0.080 69 = 0.0807 (3 s.f.) The fi rst signifi cant fi gure is 8, the second is 0 and the third is 6. The
digit to the right of the 6 is 9. 9 is more than 5 so round the 6 up to
7. You must keep the zeros at the start of the number to keep the size
of the number consistent. In this case, rounding to 3 s.f. is the same as
rounding to 4 d.p.
28 3 Place value, ordering and rounding
