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 2 − 5  2 2
Example 6: What number is divided by   to obtain   ?
3


3
Solution: Let the required number be x. Then,
 2 − 5  2 2
x ÷   =  
3

3

 2 2  2 − 5  2 − 3  3 3 27
⇒ x =   ×   =   =   = 8
3


3
3


2
27
Hence, the required number is .
8
activity
1. Divide the entire class into groups of four students each.
2. Each group will take numbered cards (2-6) from a deck of playing cards.
3. They will shuffle the cards and distribute them equally.
4. Each student will flip over one card. The first card will be the base, and the second card will be the exponent of
the first number. Similarly, the third card will be the base, and the fourth card will be the exponent of the second
number. Note that a red card represents a positive number, and a black card represents a negative number.
(Suppose, after flipping the cards, we get a red 2, a black 5, a black 4, and a red 3. Then our numbers are
3
2 and 4 .)
–5

(Base) (Exponent) (Base) (Exponent)
2 –5 (–4) 3
5. The teacher will shuffle the face cards and aces from a deck of cards, and flip the top card. Based on the
card shown, the students will do the operations as follows:
• King: Add the two numbers. • Queen: Subtract the two numbers.
• Jack: Multiply the two numbers. • Ace: Divide the two numbers.
(Suppose the teacher flips her top card and gets a Jack. Then, students will use the multiplication operation.
So the result will be 2 ×− ( 4) = 1 × − ( 64) =− ( 2) .
3
−
5
32
Each group will solve the exponents formed by their cards. The group that provides the highest number
of correct answers will be declared the winner.
Expanded Form

We have already learnt about the expanded form of whole numbers. Here, we will see how to
express it using exponents.
Let us consider a number 55346
55346 = 50000 + 5000 + 300 + 40 + 6 = 5 × 10000 + 5 × 1000 + 3 × 100 + 4 × 10 + 6 × 1

2
1
3
4
= 5 × 10 + 5 × 10 + 3 × 10 + 4 × 10 + 6 × 10 0
Similarly, we write the expanded form of decimal numbers in the same way as whole numbers.
Here, each fractional multiple of 10 is represented as a negative power.
For example, 5556.759 = 5000 + 500 + 50 + 6 + 0.7 + 0.05 + 0.009
1 1 1
= 5 × 1000 + 5 × 100 + 5 × 10 + 6 × 1 + 7 × + 5 × + 9 ×
10 100 1000

–2
–1
0
2
3
1
= 5 × 10 + 5 × 10 + 5 × 10 + 6 × 10 + 7 × 10 + 5 × 10 + 9 × 10 –3
Mathematics-8 268