Standard Index form OCR Module 8

Why is this number very difficult to use? 999,999,999,999,999,999,999,999,999,999 Too big to read Too large to comprehend Too large for calculator To get around using numbers this large, we use standard index form.

But it still not any easier to handle!?! Look at this 100,000,000,000,000,000,000,000,000,000 At the very least we can describe it as 1 with 29 noughts. But it still not any easier to handle!?!

Let’s investigate! Converting large numbers How could we turn the number 800,000,000,000 into standard index form? We can break numbers into parts to make it easier, e.g. 80 = 8 x 10 and 800 = 8 x 100 800,000,000,000 = 8 x 100,000,000,000 Size given by first number 8 and the index 11 And 100, 000,000,000 = 1011 So, 800,000,000,000 = 8 x 1011 in standard index form

So 30,000 = 3 x 104 in standard index form Try it out! How can we convert 30,000 into standard index form? Break into easier parts: And, 10,000 = 104 30000 = 3 x 10,000 So 30,000 = 3 x 104 in standard index form The number is now easier to use

Now it’s your turn: 500 = 5 x 100 = 5 x 102 4000 60,000 Copy down the following numbers, and convert them into standard index form. 500 4000 60,000 900,000 7000,000 = 5 x 100 = 5 x 102 = 4 x 1000 = 4 x 103 = 6 x 10,000 = 6 x 104 = 9 x 100,000 = 9 x 105 = 7 x 1000,000 = 7 x 106

The first number must be a value between One of the most important rules for writing numbers in standard index form is: The first number must be a value between 1 and 10 But NOT 10 itself!! For example, 39 x 106 does have a value but it’s not written in standard index form. The first number, 39, is greater than 10. Pupils should copy down rule in green

How could we convert 350,000,000 into standard index form? Again, we can break the number into smaller, more manageable parts. 350,000,000 = 3.5 x 100,000,000 100,000,000 = 108 3.5 x 100 = 350, x by 1,000,000 makes 350,000,000 350,000,000 = 3.5 x 108 in standard index form

Try it out! How can we convert 67,000 into standard index form? 10,000 = 104 67,000 = 6.7 x 104 in standard index form

Now it’s your turn: Copy out the following numbers and convert them into standard index form. 940 8,600 34, 000 570,000 1,200,000 = 9.4 x 100 = 9.4 x 102 = 8.6 x 1000 = 8.6 x 103 = 3.4 x 10,000 = 3.4 x 104 = 5.7 x 100,000 = 5.7 x 105 = 1.2 x 1000,000 = 1.2 x 106

Quick method of converting numbers to standard form For example, Converting 45,000,000,000 to standard form Place a decimal point after the first digit 4.5000000000 Count the number of digits after the decimal point. Pupil book G3 page 137 10 This is our index number (our power of 10) So, 45,000,000,000 = 4.5 x 1010

And numbers less than 1? How can we convert 0.067 into standard index form? 0.067 = 6.7 x 0.01 0.01 = 10-2 0.067 = 6.7 x 10-2

And numbers less than 1? How can we convert 0.000213 into standard index form? 0.000213 = 2.13 x 0.0001 0.0001 = 10-4 0.000213 = 2.13 x 10-4

And numbers less than 1? How can we convert 0.00603 into standard index form? 0.00603 = 6.03 x 0.001 0.0001 = 10-3 0.00603 = 6.03 x 10-3

Now it’s your turn: Copy out the following numbers and convert them into standard index form. 0.094 0.00039 0.903 0.000452 0.00624 = 9.4 x 0.01 = 9.4 x 10-2 = 3.9 x 0.0001 = 3.9 x 10-4 = 9.03 x 0.1 = 9.03 x 10-1 = 4.52 x 0.0001 = 4.52 x 10-4 = 6.24 x 0.001 = 6.24 x 10-3

Calculations

Multiply two numbers 4 x 1018 x 3 x 104 4 x 3 x 1018 x 104 = 12 x 1022 Powers of 10 4 x 3 x 1018 x 104 ADD powers = 12 x 1022 NOT Std Form! = 1.2 x 101 x 1022 = 1.2 x 1023