Year 8 Standard FormDr J Frost (jfrost@tiffin.kingston.sch.uk)

Last modified: 5th March 2014

Objectives: Appreciate the need to put big and small numbers in a more readable form, how to write numbers in standard form, and calculations involving numbers in standard form.

Associated Resources: Yr8_StandardFormQuestions.docx

111111111.... x 1111111111... =

Until you can’t enter any more digits.

3 6 =

3 +/- 4 =

What do you notice in each case?

Try these on your calculator…

www.scaleofuniverse.com

Scale of the Universe

a 10b

A number between 1 and 10 (excluding 10)

Any number (can be negative)

(No need to copy this)Standard Form is useful for two reasons:1. It allows us to write really small or really big numbers concisely...2. It allows us to compare small and big numbers.

234000000000000 23400000000000

Which is bigger?! Which is bigger?

2.34 x 1014 2.34 x 1013

Standard Form

!

We just consider how many times we’re multiplying or dividing by 10.

3 x 104 = 30,000 ?

1.24 x 105 = 124,000 ?

6 x 10-3 = 0.006 ?

Hint: Remember what happens when we have a negative index.

1.01 x 10-1 = 0.101 ?

Converting from Standard Form

Count the number of decimal point jumps to check you’ve got it right.

3.012 x 107 = 30,120,000 ?

7.5 x 101 = 75 ?

8.31 x 100 = 8.31 ?

2.4 x 10-6 = 0.0000024 ?

Check Your Understanding

How many times do we need to move the decimal point until we’re in the range 1 to 10? (excluding 10)

20000= 2 x 104 ?

0.0043= 4.3 x 10-3 ?

931,000,000= 9.31 x 108 ?

0.000001001= 1.001 x 10-6?

Converting to Standard Form

Worksheet provided.Part A and B(Part C if you finish)

Exercise

200,000,000 20 x 107 2 x 108 2 x 107

32,000 3.2 x 104 32 x 103 3.2 x 105

9 9 x 10-1 9 x 100 9 x 101

0.0001 1 x 10-3 1 x 10-4 1 x 10-5

0.012 1.2 x 10-4 12 x 10-3 1.2 x 10-2

Test Your Knowledge (Vote with your diary)

Standard Form on Your Calculator

Use the button to evaluate the following:

?

?

?

?

?

If the number at the front is not between 1 and 10 (excluding 10), it’s not in standard form. We can fix this!

200 x 104

= 2 x 102 x 104

= 2 x 106

?

?

Step 1: Convert the number at the front to standard form.

Step 2: Use laws of indices to simplify.

A faster alternative is this:

Each time we multiply this number 10...

...we have to divide this by 10 so the number overall remains the same (and vice versa)

Correcting numbers not in standard form

12×104? 0.03×105? ?

?

?

Correcting numbers not in standard formMore Examples:

(2 x 103) x (4 x 104)= 8 x 107? ?

(7 x 105) x (6 x 106)= 42 x 1011

= 4.2 x 1012 ?

?

Multiplying Numbers in Standard Form

(9 x 10-2) x (9 x 10-3)= 81 x 10-5

= 8.1 x 10-4 ?

?

Test Your Understanding

(7 x 107) x (2 x 10-3)= 14 x 104

= 1.4 x 105 ?

?

8 x 108

2 x 103= 4 x 105 ?

Dividing Numbers in Standard Form

= 5 x 106

4 x 105

8 x 10-2

?

= 0.5 x 107?

9 x 103

2 x 106= 4.5 x 10-3?

Test Your Understanding

= 2.5 x 1012

2 x 108

8 x 10-5

?

= 0.25 x 1013?

Worksheet provided.Parts C and D

Exercise