Page 12 - 新思维数学学生用书9 样章

1.1 Irrational numbers

10 a Use a calculator to find
−
+
×
+
+
−
i ( 21 )( 2 −1 ) ii ( 31 )( 31 ) iii ( 41 )( 41 ).
×
×
b Continue the pattern of the multiplications in part a.
c Generalise the results to find ( N +1 )( N −1 ) where N is a positive integer.
×
d Check your generalisation with further examples.
11 Here is a decimal: 5.020 020 002 000 020 000 020 000 002…
Arun says:
There is a regular
pattern: one zero, then
two zeros, then three
zeros, and so on. This is
a rational number.

a Is Arun correct? Give a reason for your answer.
b Compare your answer with a partner’s. Do you agree? If not, who is correct?

In this exercise, you have looked at the properties of rational and
irrational numbers.
a Are the following statements true or false?

i The sum of two integers is always an integer.
ii The sum of two rational numbers is always a rational number.
iii The sum of two irrational numbers is always an irrational

number.
b Here is a calculator answer: 3.646 153 846
The answer is rounded to 9 decimal places.
Can you decide whether the number is rational or irrational?

Summary checklist

I can use square numbers and cube numbers to estimate square roots and
cube roots.
I can say whether the square root or the cube root of a positive integer is
rational or irrational.

11