Download Write this in standard form

HIGHER – STANDARD FORM
1. Write these numbers in standard form:
(a) 827
(b) 17 632
(c) 1000 000
(d) 846 000 000 000
2. Write these numbers in standard form:
(a) 0.0001
(b) 0.03 784
(c) 0.000 000 078
(d) 0.03
3. Write these numbers out in full:
(a) 4.5 x 107
(b) 6.981 x 103
(c) 9 x 10-10
(d) 3.192 x 104
(e) 4.731 x 10-8
4. The population of China is estimated at 1100 000 000. Write this in standard form
5. A hydrogen atom weighs
0.000 000 000 000 000 000 000 001 67 grams.
Write this in standard form
6. The area of the surface of the earth is 510 000 000km2
Express this in standard form.
7. The speed of light is 300 000km/s. Express this speed in m/s and cm/s using standard form.
8. If the number 8.93 x 1015 is written out in full, how many zeros follow the 3?
Now calculate the following, and see if you can see a pattern with the indices – Calculator allowed
9. (1.4 x 107) x ( 3.4 x 1010)
10. (1.86 x 1011) x (3.21 x 104)
11. (4.22 x 108) x (1.37 x 108)
12. (2.6 x 1030) x (3.4 x 1020)
Now calculate the following, and see if you can see a pattern with the indices – NO Calculator.
13. (3 x 106) x (4 x 102)
14. (8 x 109) ÷ (4 x 103)
15. (2.5 x 1015) x (3 x 1020)
16. (2.6 x 105) + (3 x 107)
17. (3 x 1010) - (1.4 x 108)
18. (7 x 10-3) x (5 x 102)
19. (6 x 109) ÷ (4 x 103)
20. (2.5 x 10-3) x (3 x 108)
21. (1.65 x 10-8) + (3 x 10-5)
22. (3.53 x 10-5) - (2 x 10-6)
What are numbers in Standard Form?
Standard form are number in the form of 𝑎 × 10𝑏 , where a and b are values. We use standard form to write very large or
small numbers in a shorter form. ‘a’ must be between 1 and 10.
Let’s look at an example:
4 × 10³ = 4000 - here we have multiplied 4 by 10, three times. Or think of it as moving the decimal point three times to
the right.
6.7 × 106 = 6700000 – moved the decimal point six times to the right.
1.2 × 10−5 = 0.000012 – moved the decimal points five times to the left.
The last example shows that small numbers can also be written in standard form. However, instead of the index being
positive, it will be negative. The rules when writing a number in standard form is that first you write down a number
between 1 and 10, and then you write × 10(to the power of a number).
Writing numbers in Standard Form
Example 1
Write 81 900 000 000 000 in standard form:
81 900 000 000 000 = 8.19 × 1013
It’s 1013 because the decimal point has been moved 13 places to the left to get the number to be 8.19
Example 2
Write 0.000 001 2 in standard form:
0.000 001 2 = 1.2 × 10-6
It’s 10-6 because the decimal point has been moved 6 places to the right to get the number to be 1.2
Manipulation in Standard Form
This is best explained with an example:
Example
Multiply 8 × 105 with 5 × 10-2
Give your answer in standard form.
Multiply the two first bits of the numbers together and the two second bits together:
8 × 5 × 105 × 10-2
= 40 × 103 (Remember 105 × 10-2 = 103)
The question asks for the answer in standard form, but this is not standard form because the first part (the 40) should be a
number between 1 and 10. = 4 × 104