Standard Form

A number is said to be in standard form if it is re-written as a figure between 1 and 10 and then multiplied by a power of ten without changing its original value. i.e. P × 10^x.

Note

When expressing numbers in standard form, point are either carried from the left hand side (LHS) or right hand side (RHS) of it. While the point carried from the left hand side turns negative the point from right hand side turns positive.

Another very important thing to note is that when expressing either decimal number or whole number in standard form, points are carried until they are between the 1^st and 2^nd value.

Example 1; Express 263,000,000 in standard form.

Solution

The value above is a whole number so you carry point (imaginary) from (RHS) towards (LHS). Let’s do it!

= 2.63 × 10⁸. Answer


Example 2; Express 0.0006927 in standard form.

Solution

The value above is a decimal number so points are carried from the left hand side (LHS) – (RHS).

= 6.927 × 10^-4.

Example 3; Express 34.694 in standard form.

Solution

Even though the value above is also a decimal number, points here will be carried from (RHS) – (LHS).

The result will be; 3.4694 × 10¹.

Ordinary Form

Ordinary form is the opposite of standard form. When you are expressing numbers in ordinary form it means going the other way round to get your answer.

For example; Express 3.4694 × 10¹ in ordinary form.

Solution

You are going to carry the point once from (LHS) – (RHS). Why? Because 10 is raised to power of 1.

3.4694 × 10¹

= 34.694. (Answer)

Practice these questions below;

1. Express the following in standard form;

(a) 54000

(b) 0.0003164

(c) 263.478

(d) 0.00000364

(e) 600.84

2. Find the value of A if 0.000046 = A × 10^-5

3. What is the value of n if 0.0000094 = 9.4 × 10ⁿ?

4. Express the following in ordinary form;

(a) 2.83 × 10⁸

(b) 4.765 × 10^-3

(c) 1.278 × 10²

(d) 9.87 × 10^-9