Standard form: writing, multiplying and dividing numbers

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Standard Form

Write numbers in standard form- use scientific examples

multiply and divide numbers in standard form- calculation with and without a calculator. being able to interpret the calculator display.

56000000000 would be 5.6 x 10 to the power of 10

0.000000003 would be 3.45 x 10 to the power of -9.

a number in standard form must always be in exactly this form:

A x 10 to the power of n.

this number must always be between 1 and 10

this number is just the number of places the decimal point moves.

Learn the three rules:

1) the front number must always be between 1 and 10

2) the power of 10,n, is how far the decimal point moves.

3) n is positive for BIG numbers and, n is negative for small numbers.

Examples

1) express 35 600 in standard form

a) move the decimal point until 35600 becomes 3.56

b) the decimal point has moved 4 places so n=4 giving 10 to the power of 4

c) 35600 is a big number so n is +4 not -4

2) express 0.0000623 in standard form

a) the decimal point must move 5 places to give 6.23 so the power of 10 is 5

b) since 0.0000623 is a small number it must be 10 to the power of -5 not 10 to the power of +5

3) express 4.95 x 10 to the power of -3 as an ordinary number

a) the power of 10 is negative, so it's a small number. the number will be less than one.

b) the power is -3, so the decimal moves 3 places

4) what is 146.3 million in standard form?

146.3 million

=146300000

=1.463x10 to the power of 8

Multiplying and Dividing

1) rearrange to put the front numbers and the powers of 10 together

2) Multiply or divide the front numbers , and use the power rules to multiply or divide the powers of 10

3) make sure your answer is still in standard form.

examples

1) find (2.24 x 10 to the power of 3) x (6.75 x 10 to the power of 5).

(2.24 x 10 to the power of 3) x (6.75 x 10 to the power of 5).

multiply front numbers and powers seperately

= (2.24 x 6.75) x (10 to the power of 3 x 10 to the power of 5)

add the powers

= 15.12 x 10 to the power of 3+5

= 15.12 x 10 to the power of 8

15.12 not in standard form convert it

1.512 x 10 x 10 to the power of 8

= 1.512 x 10 to the power of 9

example 2

calculate 189000 / (5.4 x 10 to the power of 10)

give your answer in standard form.

189 000 / (5.4 x 10 to the power of 10)

Convert 189000 to standard form and divide numbers and powers separately.

1.89x10 to the power of 5/ 5.4 x 10 to the power of 10 = 1.89/5.4 x 10 to the power of 5 / 10 to the power of 10

subtract the powers

= 0.35 x 10 to the power of 5-10

not in standard form convert it

=0.35 x 10 to the power of -5

=3.5 x 10 to the power of -1 x 10 to the power of -5

= 3.5 x 10 to the power of -6

Comparing decimals and ordering decimals

order these decimals

0.35, 0.3, 0.3458, 0.4, 0.321, 0.41

Adding and subtracting decimals

Add these decimals together

0.45 +2.47

3.65+67.9

2.56+210.468

Subtract these decimals from each other

210.90-2.78

12.890-5.67

11.45-7.9

1239.949-128.56