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Standard Form of Large Numbers

Teacher: We can write the mass of the earth in standard form as

24
5,970,000,000,000,000,000,000,000 kg = 5.97 × 10 kg
Do you know how? Lets understand.

Scientists in different fields like Physics, Astronomy etc., have to
deal with very large numbers such as:

Distance between the Sun and the Earth that is about 149,600,000,000
m and the mass of Mars that is about 6,390,000,000,000,000,000,000,000 kg.

It is not at all convenient to read and write such large numbers. It also becomes difficult to even
compare two large numbers.

For these reasons, scientists generally write very large numbers in their standard form.

Let us learn how to write numbers in the standard form using some of the examples given below.
For examples:

24 = 2.4 × 10 = 2.4 × 10 1
240 = 2.4 × 100 = 2.4 × 10 2

2400 = 2.4 × 1000 = 2.4 × 10 3

24000 = 2.4 × 10000 = 2.4 × 10 4
5
240000 = 2.4 × 100000 = 2.4 × 10 , and so on
The numbers given above are in standard form.

The form of numbers expressed as a decimal number between 1.0 and 10.0 multiplied by the
powers of 10 is called standard form of the number.

A number is said to be in standard form if it is expressed as a × 10 , where 1 ≤ a < 10 and m is
m
an integer.

For example: 324,000,000 = 3.24 × 100,000,000 = 3.24 × 10 8
In scientific notation, the
Thus, 324,000,000 is written in the standard form as 3.24 × 10 . decimal point is placed just
8
after the left most digit of
Now, we can write the above examples in standard form as: the given number and the

11
Distance between the Sun and the Earth = 1.496 × 10 m Note: exponent of 10 is the number
one less than the number
24
Mass of Mars = 6.39 × 10 kg of digits to the left of the
decimal point of the given
The standard form of a number is also known as scientific number.
notation.

Teacher’s Reiterate the students that the exponent of 10 in the standard form of a number is equal to one less than the
Tip number of digits to the left of the decimal point. E.g., 70,040,000,000 = 7.004 × 10 10
86745.321 = 8.6745321 × 10
4

91 Exponents and Powers