Page 11 - 新思维数学学生用书9 样章

1 Number and calculation

Exercise 1.1

1 Write whether each of these numbers is an integer or an irrational number. Explain how you
know.
a 9 b 19 c 39 d 49 e 99

2 a Write the rational numbers in this list.
5
1 7 −38 160 − 225 − 35
.
12
b Write the irrational numbers in this list.
0.3333… −16 200 121 23 3 343
.
8
3 Write whether each of these numbers is an integer or a surd. Explain how you know.
a 100 b 3 100 c 1000
d 3 1000 e 10000 f 3 10000

4 Is each of these numbers rational or irrational? Give a reason for each answer.
a 2 + 2 b 22
+
c 4 + 3 4 d 3 44
+
5 Find
a two irrational numbers that add up to 0
b two irrational numbers that add up to 2.

Think like a mathematician

6 a Use a calculator to find
i 8× 2 ii 3× 12 iii 20 × 5 iv 2× 18.

b What do you notice about your answers?
c Find another multiplication similar to the multiplications in part a.
d Find similar multiplications using cube roots instead of square roots.

7 Without using a calculator, show that
a 7 < 55 < 8 b 4 < 3 100 < 5.
8 Without using a calculator, find an irrational number between
a 4 and 5 b 12 and 13.

9 Without using a calculator, estimate
a 190 to the nearest integer
b 3 190 to the nearest integer.

10