Standard Form
Video 1
Video 1
Before reading this page, YOU NEED TO KNOW HOW TO MULTIPLY AND DIVIDE BY POWERS OF 10. CHECK THAT PAGE FIRST IF YOU DO NOT KNOW.
Standard form is not hard! Standard form is just writing a number in a different way, in the standard form way.Lets say we have a number and we represent it using the letter b.
Standard form means we have to write the number b in the form a x 10n. This is saying that b is equal to a x 10n. However n must be an integer and a has to be bigger or equal to 1 and less than 10, as shown in the video.
In our example, in the video, b = 500. 500 is the number we need to put into standard form. So a has to equal 5, as 5 is bigger or equal to 1 and less than 10. How did we get 5? Use your own logic, we need a number that is bigger or equal to 1 and less than 10, which is then multiplied by 10n to get 500 and n has to be an integer.
When you have number you wish to express in standard form, find a way to reduce or increase that number so that it becomes bigger or equal to 1 and less than 10, ONLY BY MULTIPLYING OR DIVIDING BY POWERS OF 10.
The power must be an integer. So in our case, we need to to divide 500 by 102. 102 is equal to 100. So 500/100 = 5. Given we now know the number that represents a, we need to find the number that represents n. So 5 multiplied by 100 would get us 500, and 100 is equal to 102, so n = 2.
500 = 5 x 102
Lets use the same concept and idea to write 0.213 in standard form. First lets find a, by only multiplying or dividing by powers of 10, where the power is an integer. In this case, we need to multiply 0.213 by 10 to get 2.13.
0.213 x 10 = 2.13 (this number is bigger or equal to 1 and less than 10).
So now we know the value of a. Now we need to find what number multiplied by 2.13 gives 0.213. That number is 10-1, so
2.13 x 10-1 = 0.213
Remember 10-1 = 1/10
so
2.13 x 1/10 = 2.13/10 = 0.213
Thus, 0.213 in standard form is 2.13 x 10-1 .
Standard form is not hard! Standard form is just writing a number in a different way, in the standard form way.Lets say we have a number and we represent it using the letter b.
Standard form means we have to write the number b in the form a x 10n. This is saying that b is equal to a x 10n. However n must be an integer and a has to be bigger or equal to 1 and less than 10, as shown in the video.
In our example, in the video, b = 500. 500 is the number we need to put into standard form. So a has to equal 5, as 5 is bigger or equal to 1 and less than 10. How did we get 5? Use your own logic, we need a number that is bigger or equal to 1 and less than 10, which is then multiplied by 10n to get 500 and n has to be an integer.
When you have number you wish to express in standard form, find a way to reduce or increase that number so that it becomes bigger or equal to 1 and less than 10, ONLY BY MULTIPLYING OR DIVIDING BY POWERS OF 10.
The power must be an integer. So in our case, we need to to divide 500 by 102. 102 is equal to 100. So 500/100 = 5. Given we now know the number that represents a, we need to find the number that represents n. So 5 multiplied by 100 would get us 500, and 100 is equal to 102, so n = 2.
500 = 5 x 102
Lets use the same concept and idea to write 0.213 in standard form. First lets find a, by only multiplying or dividing by powers of 10, where the power is an integer. In this case, we need to multiply 0.213 by 10 to get 2.13.
0.213 x 10 = 2.13 (this number is bigger or equal to 1 and less than 10).
So now we know the value of a. Now we need to find what number multiplied by 2.13 gives 0.213. That number is 10-1, so
2.13 x 10-1 = 0.213
Remember 10-1 = 1/10
so
2.13 x 1/10 = 2.13/10 = 0.213
Thus, 0.213 in standard form is 2.13 x 10-1 .
Try answering this questions:
Write in standard form the number 0.00456
Answer:
First lets see whether we need to multiply by powers of 10 or divide by powers of 10 to get the number in the question bigger or equal to 1 and less than 10. We have to multiply 0.00456 by 103
0.00456 x 103 = 4.56
So now lets solve
4.56 x 10n = 0.00456
n = -3 because 10-3 = 1/1000
so
4.56 x 10-3= 4.56 x 1/1000 = 4.56/1000 = 0.00456