IES Rafael ReyesMaths 1º ESO

Standard Index Form

José Antonio Sayago

Objective:

To convert numbers into standard index form

Standard Index form

999,999,999,999

Why is this number very difficult to use?

Too big to readToo large to comprehendToo large for calculator

To get around using numbers this large, we use standard index form.

We can round it up to: 1,000,000,000,000

So at the very least we can describe it as 1 with 12 noughts.

But it still not any easier to handle!?!

How could we turn the number 800,000,000,000 into standard index form?

Let’s investigate!Converting large numbers

800,000,000,000 = 8 · 100,000,000,000

We can break numbers into parts to make it easier,e.g. 80 = 8 · 10 and 800 = 8 · 100

And 100, 000,000,000 = 1011

So, 800,000,000,000 = 8 · 1011 in standard index form

Try it out!How can we convert 30,000 into standard index form?

Break into easier parts:30000 = 3 · 10,000 And, 10,000 = 104

So 30,000 = 3 · 104 in standard index form

The number is now easier to use

= 9 · 100,000 = 9 · 105

Now it’s your turn:

Copy down the following numbers, and convert them into standard index form.

a)500b)4000c) 60,000d)900,000e)7000,000

= 5 · 100 = 5 · 102

= 4 · 1000 = 4 · 103

= 6 · 10,000 = 6 · 104

= 7 · 1000,000 = 7 · 106

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

For example, 39 · 106 does have a value but it’s not written in standard index form.The first number, 39, is greater than 10.

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 · 100,000,000100,000,000 = 108

350,000,000 = 3.5 · 108 in standard index form

Try it out!How can we convert 67,000 into standard index form?

67,000 = 6.7 · 10,000

10,000 = 104

67,000 = 6.7 · 104 in standard index form

Now it’s your turn:

Copy out the following numbers and convert them into standard index form.

a) 940b) 8,600c) 34, 000d) 570,000e) 1,200,000

= 9.4 · 100 = 9.4 · 102

= 8.6 · 1000 = 8.6 · 103

= 3.4 · 10,000 = 3.4 · 104= 5.7 · 100,000 = 5.7 · 105

= 1.2 · 1000,000 = 1.2 · 106

Can you find a 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.

10This is our index number (our power of 10)

So, 45,000,000,000 = 4.5 · 1010