Page 13 - 新思维数学学生用书9 样章

1 Number and calculation

1.2 Standard form

In this section you will … Key words

• learn to write large and small numbers in standard scientific notation
form. standard form

Look at these numbers:
46710 = 467 Tip
×
.
.
46710. × 2 = 467 4.67 × 10 is the
2
3
46710 = 4670 same as
×
.
46710 = 4670000 4.67 × 100 or
×
6
.
You can use powers of 10 in this way to write large numbers. For 4.67 × 10 × 10.
example, the average distance to the Sun is 149 600 000 km. You can write
8
this as 1.496 × 10 km. This is called standard form. You write a number
n
in standard form as a × 10 where 1 ⩽ a < 10 and n is an integer.
You can write small numbers in a similar way, using negative integer Tip
powers of 10. For example:
−
46710 = 0 467 Think of 4.67 × 10
1
−1
.
.
×
46710× − 2 = 0 0467 as 4.67 ÷ 10.
.
.
46710 = 0 00467
−
.
3
×
.
−
6
0
.
.
46710 = 0 00000467 Tip
×
Small numbers occur often in science. For example, the time for light to Standard form is
travel 5 metres is 0.000 000 017 seconds. In standard form, you can write also sometimes
−
8
this as 1 710 seconds.
.×
called scientific
Worked example 1.2 notation.
Write these numbers in standard form.
a 256 million b 25.6 billion c 0.000 025 6 Tip
Answer Notice that in
a 1 million = 1 000 000 or 10 6 every case the
So 256 million = 256 000 000 = 2.56 × 10 8 decimal point
b 1 billion = 1 000 000 000 or 10 9 is placed after
So 25.6 billion = 25 600 000 000 = 2.56 × 10 10 the 2, the first

c 0.000 025 6 = 2.56 × 10 −5 non-zero digit.

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