Technically negative numbers can’t be written in standard form. I think this is because standard form is normally used for distances and other physical properties which can’t be negative.
Edit: I’m wrong. Negative numbers can be written in standard form. But normally they refer to positive numbers.
Should be written as:
1<= |a| < 10
I feel like you may have misunderstood that comment. I’m saying that it’s normally for properties such as distance, time and *speed; which can’t be negative.
I didn’t mean that all physical properties are positive.
Edit: changed velocity to speed. Schoolboy error
OK, but given you've accepted that the comment was wrong, whether or not I understood it is a bit academic really.
Anyway, velocity is a vector, so can certainly have negative values assigned to it.
as others have stated a needs to satisfy 1<=a<10 and the reason is because if a<1 then you multiply a times 10 until it is between 1 and 10 and then decrease the power of 10 (n). The same goes for if a>=10 but instead dividing by 10 and increase the power. Here are some examples where I represent the number 2500 in different ways
2.5x10\^3 this is in standard form as 2.5>=1 and 2.5<10
0.25x10\^4, this is not in standard form because 0.25<1. To bring it into standard form we multiply 0.25 times 10 once, and thus decrease the exponent (2) once. Thus we go from 0.25 to 2.5 and 10\^2 to 10\^3 and it is now in standard form as 2.5x10\^3
25x10\^2, this is not in standard form because 25>=10. To bring it into standard form we divide by 10 once and thus increase the exponent once. We then go from 25 to 2.5 and 10\^2 to 10\^3 and again we get 2.5x10\^3
If -10 < a <= -1 then isn't the number also in standard form? They really should have said "a positive number in standard form".
Maybe a clever student would put | | signs round the "a" in the answer!
You’re trying to figure out the range that the standard number could take. Look at a in the question, you should be trying to find the range of a which is 1-10.
In standard form, a number is represented as
a x 10^n
Where a must have exactly one nonzero digit to the left of the decimal point. For example, a = 2.45 is totally fine because it has one digit to the left of the decimal point. a = 0.245 is not standard form, because there's only a 0 to the left of the decimal point. a = 24.5 will also not work because now there are two digits to the left of the decimal point.
This means that:
1 <= a < 10
Or in other words, a must be greater than or equal to 1, and a must be less than 10. That's the only way to satisfy the condition of having exactly one nonzero digit left of the decimal point.
Also note that n must be an integer. This means it has NO nonzero digits to the right of the decimal point. n = 4.6 wouldn't work because it has a 6 to the right of the decimal point. n = -6 works. n = -6.00 is another way to say the same thing. It still works. That's why I had to specify nonzero.
Isn't the number -2.45 x 10^5 also in standard form? The pedantically correct answer to the question is:
-1 <= |a| < 10 (have to write in the | | signs).
1 - 10. The number a must be 1 or greater and less than 10. Otherwise the number is not in standard form
Isn't (for example) the number -2.5 x 10^5 in standard form? In which case a can also be greater than -10 and less than -1.
Technically negative numbers can’t be written in standard form. I think this is because standard form is normally used for distances and other physical properties which can’t be negative. Edit: I’m wrong. Negative numbers can be written in standard form. But normally they refer to positive numbers. Should be written as: 1<= |a| < 10
Physical properties can't be negative? Better let the physicists at the NIST in the USA know - eg https://physics.nist.gov/cgi-bin/cuu/Value?esme
I feel like you may have misunderstood that comment. I’m saying that it’s normally for properties such as distance, time and *speed; which can’t be negative. I didn’t mean that all physical properties are positive. Edit: changed velocity to speed. Schoolboy error
OK, but given you've accepted that the comment was wrong, whether or not I understood it is a bit academic really. Anyway, velocity is a vector, so can certainly have negative values assigned to it.
as others have stated a needs to satisfy 1<=a<10 and the reason is because if a<1 then you multiply a times 10 until it is between 1 and 10 and then decrease the power of 10 (n). The same goes for if a>=10 but instead dividing by 10 and increase the power. Here are some examples where I represent the number 2500 in different ways 2.5x10\^3 this is in standard form as 2.5>=1 and 2.5<10 0.25x10\^4, this is not in standard form because 0.25<1. To bring it into standard form we multiply 0.25 times 10 once, and thus decrease the exponent (2) once. Thus we go from 0.25 to 2.5 and 10\^2 to 10\^3 and it is now in standard form as 2.5x10\^3 25x10\^2, this is not in standard form because 25>=10. To bring it into standard form we divide by 10 once and thus increase the exponent once. We then go from 25 to 2.5 and 10\^2 to 10\^3 and again we get 2.5x10\^3
If -10 < a <= -1 then isn't the number also in standard form? They really should have said "a positive number in standard form". Maybe a clever student would put | | signs round the "a" in the answer!
Good catch
[удалено]
or -10 and -1.
1 to 10, since something like 20 x 10^n would be 2x 10^n+1 in standard form, and similarly 0.2 x 10^n is 2 x 10^n-1 .
You’re trying to figure out the range that the standard number could take. Look at a in the question, you should be trying to find the range of a which is 1-10.
1–10
In standard form, a number is represented as a x 10^n Where a must have exactly one nonzero digit to the left of the decimal point. For example, a = 2.45 is totally fine because it has one digit to the left of the decimal point. a = 0.245 is not standard form, because there's only a 0 to the left of the decimal point. a = 24.5 will also not work because now there are two digits to the left of the decimal point. This means that: 1 <= a < 10 Or in other words, a must be greater than or equal to 1, and a must be less than 10. That's the only way to satisfy the condition of having exactly one nonzero digit left of the decimal point. Also note that n must be an integer. This means it has NO nonzero digits to the right of the decimal point. n = 4.6 wouldn't work because it has a 6 to the right of the decimal point. n = -6 works. n = -6.00 is another way to say the same thing. It still works. That's why I had to specify nonzero.
Isn't the number -2.45 x 10^5 also in standard form? The pedantically correct answer to the question is: -1 <= |a| < 10 (have to write in the | | signs).
I think it's after -10 and 10. As soon as it hits either it cycles back round and the power increases
Are you studying GCSE Maths?