Standard Form HELP!?

Question

Today we were told to revise standard form but some of it I really don't understand. It's probably just a silly misunderstanding but could someone say it in plain and clear.

One of the questions: 52100 in standard form and the answer is 5.21 x 10 to the power of 4.


Our teacher said the dec pl. has to be between 1 - 10. But then wouldn't 52.1 be between one and ten?

Please explain as I have a test!

Answer 1

You've pretty much got the answer. Standard form is all about taking a number with zeros such as 52100 and doing what you've done.

But the bit about it being about 1 to 10 is about the number as a whole.

E.g.

52100 is not between 1 and 10
5210 is not between 1 and 10
521 is not between 1 and 10
52.1 is not between 1 and 10

5.21 is between 1 and 10, so we use that.

Keep dividing by 10, until the number you're dealing with is between 1 and 10.

So with this, your answer in standard form would be:

52100 = 5.21 x 10 to the power of 4.

Answer 2

52.1 is not between 1 and 10 as 52 is more than 10. Your teacher was right: the decimal pt has to come after the first digit (eg 943 would be 9.43 x10 to the power 2 and 46300 would be 4.63 x 10 to the power 4 and 37.21 would be 3.721 x 10 to the power 1. Note, the power is always one number less than there are numbers in front of the decimal point in the original number.943 has 3 digits so the power is 2. 46300 has 5 digits so the power is 4, 37.21 has only 2 digits in front of the decimal pt so the power is 1. Good luck with the test!

Answer 3

You're almost right: in standard form, it's the number before the x sign that has to be between 1 and 10. Therefore you have to adjust the power of 10 until that condition is satisfied.

52.1 would be 5.2 x 10^1 in standard form.

Answer 4

i could put it another way

standard form is where you write each number in a format that has one non zero digit at the beginning BEFORE the decimal point and all the other digits AFTER the decimal point

so for 52100 the first digit is a 5 so you put that down followed by a decimal point

so you then write down the other numbers after 5 which are also after the decimal point

so you get 5.2100

but we can dispense with the last two zeros to get

5.21

then as this has been reduced by a multiple of 10 we need to put that into the number to account for it

the decimal place has been moved 4 places to the left so we need to multiply the number by 10^4

so in standard form we would write 52100 as 5.21 x 10^4

Answer 5

Either you need to round it off to 5.2 x 10^4 or write it as 52.1 x 10^3 but then that is not a standard form.

Check some other examples given by your teacher.

Answer 6

He means one through ten which it would be 5.2 times 10 to the power of four lets say * is multiplication okay
then it would be 5.2 x 10 with the four on top of the ten like it has the power of ten call me if u need help at 3871547 im willing to help

Answer 7

52.1 would be right because the two zero's would not count so 52.1 would be right