Cambridge International Mathematics

Assumed Knowledge (Number) 23

5 Find the answer correct to the number of decimal places shown in square brackets:

a^174 [1] b^738 [2] c 4 : 3 £ 2 :6 [1]

d 0 : 12 £ 0 :4 [2] e 118 [2] f 0 : 08 £ 0 :31 [3]

g (0:7)^2 [1] h^376 [2] i^177 [3]

6 In her maths exam Julie was asked to round 7 : 45 cm to one decimal place and to the nearest whole

integer.

Julie’s answer was that 7 : 45 cm¼ 7 : 5 cm (to one decimal place), and that 7 : 5 cm¼ 8 cm (to the

nearest whole number).

Explain what Julie has done wrong and why we need to be careful when we make approximations.

SIGNIFICANT FIGURE ROUNDING

The firstsignificant figureof a decimal number is the first (left-most) non-zero digit.

For example: ² the first significant figure of 1234 is 1

² the first significant figure of 0 :023 45is 2.

Every digit to the right of the first significant figure is regarded as another significant figure.

Procedure for rounding off to significant figures:

Count off the specified number of significant figures then look at the next digit.

² If the digit is less than 5 , do not change the last significant figure.

² If the digit is 5 or more then increase the last significant figure by 1.

Delete all figures following the significant figures, replacing with 0 s where necessary.

Notice that if 13 : 238 is rounded to 13 : 24 , then it has been rounded to 2 decimal places or to 4 significant

figures.

Example 31 Self Tutor

Round: a 5 : 371 to 2 significant figures b 0 : 0086 to 1 significant figure

c 423 to 1 significant figure

a 5 : 371 ¼ 5 : 4 ( 2 s.f.)

This is the 2 nd significant figure, so we look at the next digit which is 7.

The 7 tells us to round the 3 to a 4 and leave off the remaining digits.

b 0 : 0086 ¼ 0 : 009 ( 1 s.f.)

These zeros at the front are place holders and so must stay. The first significant figure is the 8.

The next digit is 6 , which tells us to round the 8 to a 9 and leave off the remaining digits.

c 423 ¼ 400 ( 1 s.f.)

4 is the first significant figure so it has to be rounded. The second digit, 2 , tells us to keep the

original 4. We convert the 23 into 00. These two zeros are place holders; they are not ‘significant

figures’ but need to be there to make sure the 4 still represents 4 hundreds.

IGCSE01

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