Lesson 7, Topic 1
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# Standard Index Form – Numbers Greater than 1

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Standard index form is a way of expressing numbers as a product of two terms: The first term being a number between 1 and 10 and the second part is a power of 10.

In general, it is expressed as $$\scriptsize \; a \; \times \; 10^n \!\!\;$$where a is a number between 1 and 10 an n is an integer which can be positive, negative or zero.

### Numbers Greater Than 1:

Every number has a decimal point usually at the back of the last digit of the number. E.g. 15, the decimal point is after 5. Also, 706 the decimal point is after 6.

Example 1

Express these numbers in standard form

a. 25 000 000

b. 5 000

c. 7

d. 270,000

e. 15

Solution

a. 25 000 000

Step 1: Move the decimal point to the back of the first significant digit

Step 2: Count the number of movements made from the initial position of the decimal point.

=   2.5 x 107

b. 5 000

= 5 x 103

c. 7

There is 0 movement

therefore the power of 10, in this case, is 0.

= 7 x 100

d.270,000

=  2.7 x 105

e. 15

1.5 x 101

Example 2

Express the following in standard form.

a. 18.902

b. 40 830

c. 5123.59

d. 193.25

Solution

a. 18.902

=  1.8902 x 101

b. 40 830

=  4.0830 x 104

c. 5123.59

= 5.12359 x 103

d. 193.25

= 1.9325 x 102

Example 3

Change these standard forms to ordinary numbers.

a. 6 x 105

b. 2.3×104

c. 1.05×106

d. 7003 x104

Solution

a. 6 x 10

= 6 x 10 x 10 x 10 x 10 x 10

= 6 x 100 000

= 600 000

b. 2.3 x 10

= 23 000

c. 1.05 x 10

= 1 050 000

d. 7003 x 104

= 70 030 000

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