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Standard Form. A number expressed in standard form is a number written between 1 and 10 multiplied by 10 to an appropriate power. The use of standard form is to represent very small numbers or very large numbers. For example 0.000 000 000 000 32 represented in standard form will be.

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standard form

Standard Form

A number expressed in standard form is a number written between 1 and 10 multiplied by 10 to an appropriate power.

The use of standard form is to represent very small numbers or very large numbers

For example

0.000 000 000 000 32 represented in standard form will be

214000 000 000 represented in standard form will be

slide2

Example

  • Express each of the following in standard form
  • 0.000 000 462
  • 0.004
  • 90 000
  • 5910 000 000
slide3

Example

Express each of the following as ordinary numbers

(i)

(ii)

(iii)

(iv)

slide4

Example

Write the following list in order of size starting with the smallest

  • , 27 000 000, , 0.000 44,
slide5

Example

The surface of the earth is about 509 970 000 km2. Express this in standard form correct to two significant figures.

slide6

Example

  • Without a calculator work out the following and give your answer in standard form.
  • (a) 30 x 40 000
  • (b) 12 000 x 0.00005
  • (c)
  • (d)
  • (e)
slide8

Example

Given that and work out, without a calculator

(i) (ii)

slide9

1

.

2

EXP

5

5

EXP

9

  • Example
  • Given that and
  • work out , in standard form
  • (i) (ii)

Here we use the button for the standard form and type for X

EXP

And for Y we type

slide10

Example

  • A rectangle has length AB = km and width BC = km.
  • Giving your answer in standard form, find
  • the area,
  • the perimeter of this rectangle.
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