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Standard Form. 2 is multiplied by itself 3 times. Revision. Powers:. On calculator:. Try these:. 6 5. 5 4. 3 6. 2 5. 9 4. 10 4. 10 000. Answers:. 7776. 625. 729. 32. 6561. 3 zeros. Powers of 10. Powers of 10 are easy. e.g.10 3 = 10 x 10 x 10 =1000.

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Standard form

Standard Form


Standard form

2 is multiplied by itself 3 times

Revision

Powers:

On calculator:

Try these:

65

54

36

25

94

104

10 000

Answers:

7776

625

729

32

6561


Standard form

3 zeros

Powers of 10

Powers of 10 are easy

e.g.103 = 10 x 10 x 10=1000

Look at these sequences

Divide by 10

From this we see that


Standard form

Working with big numbers

Scientists often have to work with big numbers.

Example:

The distance the earth travels in one orbit is 558 000 000 miles.

We can express this number in a more concise form as follows.

558 000 000 = 5.58 x 100 000 000 = 5.58 x 108

is said to be in

Standard Form

5.58 x 108

or

Scientific Notation

is said to be in

Normal Form

558 000 000


Standard form

the power is a positive or negative whole number

exactly one digit before the point

watch this

5 jumps

63.

x 105

630.

6300.

630000.

63000.

2

1

3

4

5

Look at this number which is in Standard Form

6.3 x 105

6.3 x 105

= 630 000

= 6.3 x 10 x 10 x 10 x 10 x 10

Standard form

Ordinary Number

6.3


Standard form

Example:

Write 2.45 x 104 as an ordinary number.

  • Write the question

  • List the digits without the point

  • 4 jumps from position of “old” point

  • Write the answer

Method:

Add zeros as required

0

0

0

0

2 4 5

1

3

4

2

Now try these:

Write as ordinary numbers:

4 x 103

4.88 x 101

1.47 x 102

9.08 x 106

1.3 x 100

147

9080000

1.3

4000

48.8


Standard form

4

1

5

3

2

watch this

5 jumps

Therefore

630 000

= 6.3 x 105

x 105

Ordinary Number

Standard form

630 000

= 6.3 x 100 000

= 6.3 x 105

63000.

630000.

0

0

0

6300.

0

0

0

0

0

0

0

0

0

0

0

630.

6.3

63.


Standard form

Make the number “look” like standard form

Positive power since large number

Put in a decimal point to make the number “look” like a number between 1 and 10.

= 2 7 0 6

Example:

Write 2706 in standard form.

Method:

  • Write the number

  • Insert “new” decimal point

  • Count jumps to position of “old” decimal point

2 7 0 6

3

2

1

x

3

10

Now try these:

Write in standard form:

34560

1023.6

12.8

4.6

230000

3.456 x 104

1.0236 x 103

1.28 x 101

4.6 x 100

2.3 x 105


Standard form

the power is a positive or negative whole number

exactly one digit before the point

watch this

3 jumps

x 10-3

1

2

3

Numbers less than 1

Consider the number

2.03 x 10-3

This number is in standard form but is different from previous examples.

Look again at powers of 10

Notice the power is negative

= 0.00203

2.03 x 10-3

= 2.03 x 0.001

Standard form

Ordinary Number

x 10-3

2.03

.203

.0203

.00203

= 0.00203


Standard form

Example:

Write 1.07 x 10-4 as an ordinary number.

  • Write the question

  • List the digits without the point

  • 4 jumps from position of “old” point

  • Write the answer

Method:

Add zeros as required

That means the answer starts with 0.-----

Note: When the power is negative the ordinary number is always less than 1.

0

0

0

1

3

4

2

0

1 0 7

0

0

0

Now try these:

Write as ordinary numbers:

4.081 x 10-4

4 x 10-3

1.47 x 10-2

9.08 x 10-5

1.3 x 10-1

0.0147

0.0000908

0.13

0.004

0.0004081


Standard form

1

3

2

watch this

3 jumps

Therefore

630 000

= 6.31 x 10-3

x 10-3

Ordinary Number

Standard form

0.00631

= 6.31 x 0.001

= 6.31 x 10-3

0.00631

0

0

0

0.631

0.0631

0

0

0

6.31


Standard form

Make the number “look” like standard form

0 0 0 2 7

Negative power since tiny number

Put in a decimal point to make the number “look” like a number between 1 and 10.

= 2 7

Example:

Write 0.0027 in standard form.

Method:

  • Write the number

  • Insert “new” decimal point

  • Count jumps to position of “old” decimal point

3

2

1

3

x

10

-

Now try these:

Write in standard form:

0.3456

0.00102

0.0128

0.000046

0.0000000023

3.456 x 10-1

1.02 x 10-3

1.28 x 10-2

4.6 x 10-5

2.3 x 10-9


Standard form

We use EXP button as shown on the calculator to enter numbers already in standard form.

2 6 EXP 8 =

check this is correct

Too large to convert

3 5 EXP 1 2 =

Standard Form on the Calculator

Examples:

2.6 x 108

260 000 000

3.5 x 1012

Calculator’s way of writing 3.5 x 1012 – does not mean 3.5 to the power 12!

3.5 12


Standard form

calculator display

calculator display

(2.484 x 107) (4.6 x 10-4)

  • Only enter EXP before power, never x 10 EXP

  • For negative powers use the ( - ) key not the key, we are not subtracting.

Calculations Giving your Answer in Standard Form

Example 1:

(2.6 x 108) x (4.2 x 106)

= 1.092 x 1015

1.092 15

Example 2:

= 5.4 x 1010

5.4 10

Note:

See calculators again

  • Remember to change number on display to ---- x 10--

Click button to end presentation


Standard form

( - )


Standard form

END


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