1. Understand and use standard form for very large and very small numbers
If you have any questions regarding these resources or come across any errors, please contact

2. Key vocabulary Power Index notation Standard index form
Scientific notation

3. Big numbers in standard form
To write in standard form we must have a number between 1 and 10 x 10 to the power of a number
Move the point to get a number between 1 and 10
The index number should represent the number of spaces we moved the decimal point . .
= 3 x 10 6
Write the
decimal point at the end first (it will be moved)
This number should be between 1 and 10

4. Big number practice
7 x 10⁵
9.1 x 10⁴
3.23 x 10⁶
4.58 x 10⁶
1.214 x 10⁷

5. Small numbers in standard form
Write in standard form.
Move the point to get a
number between 1 and 10 and count the jumps back to the original decimal place
We use a negative power when converting small numbers to SF
The index number should represent the number of jumps from new decimal place to original decimal place .
= 2.3 x 10 ¯6
This number should be between 1 and 10

6. Small number practice
3.5 x 10 ¯⁵
2.5 x 10 ¯³
6 x 10 ¯⁸
7.89 x 10 ¯⁶
1.24 x 10 ¯⁹

7. Multiply using standard form
Remember the rules for multiplying indices
(4 x 108) x (5 x 10⁴)
4 x 108 x 5 x 104
Multiply Numbers
Multiply Powers of 10
4 x 5
x 108 x 104
ADD powers
= 20
x 1012
÷10
x10
NOT Standard Form
= 2.0 x 1013

8. Multiply practice (3x 102) x (7 x 105) 2.1 x 10⁸

9. Divide using standard form
(44 x 108) ÷ (4 x 10⁴)
Divide numbers
Divide Powers of 10
44 ÷4
108 ÷ 104
subtract powers
= 11
x 10⁴
x10
÷10
NOT Standard Form
= 1.1 x 10⁵

10. Divide practice
5 x 10⁵
(45 x 10⁷)÷(9 x 10²) (36 x 10⁵)÷(4 x 10⁹) (33 x 10⁷⁸)÷(11 x 10⁹) (60 x 10²)÷(6 x 10⁹)
9 x 10¯⁴
3 x 10⁶⁹
1 x 10¯6

11. Add / subtract using standard form
5 x 10⁴
If the powers are the same you can just add the big numbers and keep the powers the same!
+ 3 x 10 ⁴
_______________ 8
x 10 ⁴
If the exponents are not the same convert the numbers to whole numbers and then add / subtract
4 x 10⁹
_______________
- 3 x 105
= x 10⁹
_______________

12. Add / subtract practice
(2.53 × 10 ⁹ ) + (7.61 × 10⁸ )
(2.86 × 10³ ) + (7.55 × 10⁶ )
(2.24 × 10² ) + (9.92 × 10² )
(1.35 × 10 ¯⁸ ) + (6.82 × 10 ¯⁸ )
3.291 × 10⁹
× 10⁶
1.216 x 103
8.17 × 10 ¯⁸
(1.53 × 10¯³ ) - (2.41 × 10¯⁴ )
(8.22 × 10 ¯⁴ ) - (8.33 × 10 ¯⁵ )
(2.75 × 10 ¯⁴ ) - (4.89 × 10 ¯⁷ )
1.289 × 10¯³
7.387 × 10 ¯⁴
× 10 ¯⁴

13. Problem solving and reasoning
Dinosaurs lived between 65 million years ago, in a time known as the Mesozoic Era. Write this in standard form.
6.5 x 107
Light travels at a constant, finite speed of 186,000 miles per second. Using standard form, multiply this by (1.3 x 10⁵).
2.418 x 1010
A super rocket is going to travel from Earth to Jupiter and then to the Kuiper Belt. If the distance from earth to Jupiter is 2.9x1010m and from Jupiter to the Kuiper Belt is 9.9 x 109m
What is the total distance it will travel? 3.89 x 1010
If its speed is 100m/s how long will the journey take? 3.89 x 10⁸ seconds

14. Exam specimen questions

15. Exam specimen questions

16. Exam specimen questions

17. Exam specimen questions

18. Exam specimen questions

19. Exam specimen questions

20. Exam specimen questions

21. Exam specimen questions

22. Exam specimen questions

23. Exam specimen questions

24. Exam specimen questions