Page 26 - Math 7

Number Systems in Diff erent Bases

Let’s take 17 blocks of cubes and regroup them into the group of 10 blocks.

17 = 10 + 7 = 1 × 10 + 7 × 10°
1

Let’s take 39 pencils and regroup them into the group of 10 blocks.

1
39 = 30 + 9 = 3 × 10 + 9 × 10°
0
Similarly, 594 = 500 + 90 + 4 = 5 × 10 + 9 × 10 + 4 × 10 .
2
1
In this way, whole numbers can be regrouped into the base of 10 with some power
of 10. It is called the decimal numeration system or denary system.
Each digit of a numeral has its own place and its place value is obtained multiplying
the digit by its place. For example, let's take a numeral 7425.
7425

It is at ones place and place value is 5 × 1 = 5
It is at tens place and place value is 2 × 10 = 20
It is at hundreds place and place value is 4 × 100 = 400
It is at thousands place and place value is 7 × 1000 = 7000
Now, we can write the numeral 7425 in the expanded form in the following way.
7425 = 7 × 1000 + 4 × 100 + 2 × 10 + 5 × 1
= 7 × 10 + 4 × 10 + 2 × 10 + 5 × 10°
3
2
1
In this way, if x, y and z are the digits at hundreds, tens and ones place respectively
in a number, then the number can be expressed as 100x + 10y + z.
2.3 Periods and place

The tables given below show the periods and places in Nepali system and
International system of numerations.

9 1 6 7 2 4 3 8 5 6 3 0

9 1 6 7 2 4 3 8 5 6 3 0

Vedanta Excel in Mathematics - Book 7 24 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur