Page 158 - Start Up Mathematics_6

8 Decimals

Decimals play a very important role in Mathematics. The word decimal is derived from the Latin word
decem meaning ten. Most of us do not realize that we use decimals in our day to day life. Can you
recollect your parents giving you right dose of cough syrup using a dosing cup with various markings
i.e., 2.5 mL, 5 mL, 7.5 mL, etc? Intuitively, one can make out 2.5 mL is exactly between 2 mL and
3 mL. Similarly, the dot in ` 116.75 is the decimal point. Also ` 116.75 = ` (116 +.75) = ` 116 and
75 paise.

In this chapter, we will learn how decimals are an extension of base-ten system and explore the
relationship between fractions and decimals. We will also learn comparison of decimals, operations
on decimals and applications of decimals.

Tenths

In a place value table on moving a digit from the right to the left by one place, its place value
becomes ten times. Similarly, on moving a digit from the left to the right by one place, its place
value becomes one-tenth.
Let’s observe the Indian place value chart once again:

LAKHS THOUSANDS ONES
Ten Lakh Lakh Ten Thousand Thousand Hundred Ten One
10,00,000 1,00,000 10,000 1,000 100 10 1
In this chart, place value of thousand = one-tenth of ten thousand
Place value of one = one-tenth of ten

Have you ever thought of a place right to ones? What value will the digit right to ones attain?
Obviously, it will be one-tenth of ones.
1
One-tenth is also written as or 0.1 and ‘.’ is read as point or decimal.
10

1
or 0.1 is division of a unit into ten equal parts.
10

Let’s consider the given strip as 1. Therefore, the coloured
1
part is .
10

The Indian place value chart is extended further as:

LAKHS THOUSANDS ONES
Ten Lakh Lakh Ten Thousand Thousand Hundred Ten One Tenth Hundredth
1 1
10,00,000 1,00,000 10,000 1,000 100 10 1
10 100