Need help with indices.?

Question

Could anyone please give me an answer to this questions.

1. the population of china is 1.3 billion(1,300,00,00). write this using indices : 13x__

2. the distance from the earth to the sun is 150,000,000km. write this using indices : 15x10__

thank you.
and if you could, could you guys also give me the basic explanation on how indices work :)
sorry i'm not too good in maths haha..

Answer 1

First remind yourself of these powers (also called indices)

10,000 = 10*10*10*10 = 10^4

Each time we divide by 10 the power reduces by 1

1,000 = 10*10*10 = 10^3

100 = 10*10 = 10^2

10 = 10^1

1 = 10^0

and following the same pattern

1/10 = 10^-1

1/100 = 10^-2

1/1000 = 10^-3 and so on.



Engineers often reduce large numbers to a form A * 10^n, where A is a number between 10 and 100

Example 1: 70,000,000 in this "engineers" form is 70 * 10^6



To do this follow these simple rules:

a) Select the number between 10 and 100 at the beginning, (in this case 70), and imagine a decimal point after it.

b) Carefully count the number of places you have to move the decimal point to get to the end.

In example 1 you have to jump over 6 more zeros after the 70 so the power of 10 is 6 and you write that next to the 70 as 70 * 10^6



By the way you made a small MISTAKE COPYING 1.3 billion but I have put it right below.

Also, although standard form is widely used this question asks you to use a different form.



1. The population of China is 1.3 billion(1,300,000,000). write this using indices : 13x__

13 and 8 jumps over zeros so we write 13 * 10^8



2.

The distance from the Earth to the sun is 150,000,000 km. write this using indices : 15x10__

Time for you to join in.

15 and 7 jumps over zeros so you will have no trouble working out that you should write

................. ?????



Regards - Ian

Answer 2

What you mean is that you want them written in Scientific Notation, or Standard Form. The population of China is not 1,300,00,000 - it is 1,300,000,000 and that is 1.3 x 10^9 - rewrite the number with only 1 figure to the left of the decimal point, x a power of 10 the index is the number of places you have moved the decimal point (although it is not written it is understood to be 1,300,000,000.0

Answer 3

you're fine, be brave!



1.3 x 10^9 ; it's 9 zeroes after the whole number part, (the decimal part doesn't count!)



OR 13 x 10^8, says add 8 zeroes after the 13.

Think of 2x100 = 200 that's = 2x10^2 (see how the 2 is the same number of zeroes?!)



you just need to be careful when there is a decimal, it's the whole number part that is important!



good luck!

Answer 4

13x10^6 and 15x10^7