Page 7 - 新思维数学活动用书9 样章

1 Number and calculation

Practice

5 a Find 1.5 2
b Show that 225. is a rational number.
c Is 20 25. a rational number? Give a reason for your answer.

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d Is 1 331. a rational number? Give a reason for your answer.
6 Without using a calculator, show that
a 3 < 3 41 < 4 b 9 < 3 800 < 10 c 1 1. < 1 36 < 12.
.
.
7 Without using a calculator, find an irrational number between
a 2 and 3 b 6 and 7 c 1.4 and 1.5.
8 Without using a calculator, estimate
a 140 to the nearest integer
b 3 350 to the nearest integer.

9 Arun says:

My calculator shows
7
2 =2.086 419 753 and
81
this does not have a
7
repeating pattern, so 2
81
is irrational.

a Is Arun correct? Give a reason for your answer.

b Do you think 2 7 is a rational number? Give a reason for your answer.
81

Challenge

10 a Use a calculator to show that 2 × 32 is a rational number.
b Find two irrational numbers with a product of
i 6 ii 9 iii 10.
11 a Explain why 5 + 2 is an irrational number. Tip

b Find two irrational numbers with a sum of 5. Write 5 + 2 as
c Explain why it is impossible to find two rational numbers with a decimal.
a sum of 5.

d Is it possible to find two rational numbers with a product of 5?
Give a reason for your answer.

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