Good day my students, in this post you'll know how to solve standard form problems. In standard form, the main concept there is numbers in power of 10 either positive or negative, positive (+) and negative (-).Numbers expressed in the form A x 10ⁿ where A is between 0 and 10 and n can either be positive or negative is said to be in standard form.
We say, standard form is expressed as a product of a digit and power of 10.
300
= 3 x 100
= 3 x 10²
This is because 10 is raised to power 2, in 300 we have 2 zeros, remember we only have 2 zeros in hundred.
what about this:
Express these in standard form
ii. 23.12
i.1203
iii. 3. 345
Solution
1. 23.12
= 23 . 12
2.312 x 10¹
Note : In any given number, after the first digit include x sign before 10 and raise with positive number or negative.
In 2 3 . 12 ------------ 23 is a whole number while 12 is remainder, consider 23 as 20 + 3 , here we have only 1 ten. That is why i raised it by 1.
2.1203
= 1203
= 1 . 203 x 10³
Yesss, this one also must be noted, here we have 1000 + 200+ 30 , in 1203 we have 000 in thousand.
,iii. 3. 345
= 3. 345
3. 345 x 10º
Wow, that means no 10 in 3 so i raised it to power 0 (zero).
I so much belief you understand that simple-method in solving standard form issues
Now let's take a look at some other examples based on powers of 10 in index form.
powers of 10 in index form
and so on....
100 000 = 10 x 10 x 10 x 10 x 10 = 10⁵
10 000 = 10 x 10 x 10 x 10 =10⁴
1 000 = 10 x 10 x 10 =10³ -------------Positive powers
1 00 = 10 x 10 = 10²
10 = 10 = 10¹
1 = 1 =10º
0 .1 = 1/10 = 10⁻¹
0.01 = 1/100 = 10⁻²
0.001 = 1/1000 = 10⁻³
0.000 = 1/ 10000 = 10⁻⁴
and so on....
Express these in standard form
a. 0 .234
b.255 000
c.0.000023
d. 12730
Solution
a. 0 .234
2.34 2.34
= ----------- = ----------- = 2.34 x 10⁻¹
10 10¹
b.255 000
2.55 x 100000
= 2.55 x 10⁵
In 255 we have 2 zero (00) that is in two hundreds, added with the remaining three zero that is why i raised it to power 5.
c.0.000023
2. 3
= -------------------
100000
2. 3
----------------
10⁵
= 2. 3 x 10⁻⁵
d. 12730
= 1.2 x 10⁴
Now solve these
Express the following in standard form
a. 34 . 23
b. 0.0034
c. 230
d.4.23
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