Standard Form

A particular number is said or observed to be in standard form if it is written in this form:
V x 10ⁿ.

1 ≤ V < 10
Where V can be in positive/negative whole number or positive/negative decimal number.

(ⁿ) is the number of times a point moves either on the LEFT hand side or at the RIGHT hand side of a particular number. It can be either positive (+) or negative (-)

Example 1 (Standard form):

Express the following in the standard form:
(a) 648000000 (b) 0.000064836 (c) 0.647 (d) 78.648 (e) 9.0678

Solution

(a) 648000000

= V x 10ⁿ

First step:
Place a point(.) after the last digit of that number: 648000000.

Second step:
Now, move the point to the left hand side (L H S) and record how many times the point moves. If the point moves to the RIGHT, (ⁿ) will have a negative sign, but if it moves to the LEFT it has a positive sign.
That is:
64800000.0 x 10¹
6480000.00 x 10²
648000.000 x 10³
64800.0000 x 10⁴
6480.00000 x 10^5
648.000000 x 10^6
64.8 x 10^7
648000000 = 6.48 x 10^8

(b) 0.000064836

Solution:
Use the same approach in example (1a), but now you have to count from left, move the point and continue recording the number of times it moves towards the RIGHT hand side. The (ⁿ) will be in negative because we are now moving from left to right.

0.000064836 x 10°
00.00064836 x 10–¹
000.0064836 x 10–²
0000.064836 x 10–³
00000.64836 x 10–⁴
0.000064836 = 6.4836 x 10^–5 (Ten raised to power minus five)

(c) 0.647

0.647 = 6. 47 x 10–¹

(d) 78.648

78.648 = 7.8648 x 10¹

(e) 9.0678

9.0678 = 9.0678 x 10°

QUESTIONS AND SOLUTIONS (Standard form):

Q1: Express the following in standard form:

(a) 54000
= 5.4 x 10⁴

(b) 0.0003164
= 3.164 x 10–⁴

(c) 263.478
= 2.63478 x 10²

(d) 0.00000364
= 3.64 x 10^–6

(e) 600.84
= 6.0084 x 10²

Q2: Find the values of the following:

(a) 4.06 x 10^11
= 406000000000

(b) 2.04 x 10^–5
= 0.0000204

(c) 6.14 x 10^–9
= 0.00000000614

Q3: Find the value of A if 0.000046 = A x 10^–5

Solution:
4.6 x 10^–5 = A x 10^–5
A = 4.6

Q4: What is the value of n if 0.0000094 = 9.4 x 10ⁿ

Solution:
9.4 x 10^–6 = 9.4 x 10^–6
n = -6

Q5: Express in standard form 0.00008532

Solution:
0.00008532 = 8.532 x 10^–5

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