DECIMALS - UNDERSTANDING TENTHS, HUNDREDTHS, THOUSANDTHS ETC., PROBLEMS, LINKS

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Please study Fractions before Decimals,
if you have not already done so.

What we study here is extension of Fractions.

Extension of Fractions

Let us study fractions with denominator 10.
Look at the following figure.

                                                                                                                        


            In the above figure,
            the blocks are 1 black, 2 green, 3 blue, 4 red.

            So, the portion of each colour compared to the whole is
            black = 1⁄10; green = 2⁄10; blue = 3⁄10; red = 4⁄10;

             black + red = 1⁄10; + 4⁄10; = 5⁄10;
             green + red = 2⁄10; + 4⁄10; = 6⁄10;
             blue + red = 3⁄10; + 4⁄10; = 7⁄10;
            black + blue + red = 1⁄10; + 3⁄10; + 4⁄10; = 8⁄10;
            green + blue + red = 2⁄10; + 3⁄10; + 4⁄10; = 9⁄10;

These fractions with denominator of 10 have a speciality.

Tenths

The fractions with 10 as denominator are called tenths.

We know
10 milli metres (mm) = 1 centi metre (cm)
or 1 mm = 1⁄10 cm or one-tenth cm ;
or 3 mm = 3⁄10 cm or three-tenth cm

10 Quintals = 1 metric tonne
or 1 Quintal = 1⁄10 metric tonne ; or 7 Quintals = 7⁄10 metric tonne

We also write the fractional number 1⁄10 (one-tenth)
as .1 read as decimal one or point one.

Similarly, we write the fractional number 2⁄10 (two-tenth)
as .2 read as point two.

Like wise,
3⁄10 (three-tenth) = .3 read as point three.
4⁄10 (four-tenth) = .4 read as point four.
5⁄10 (five-tenth) = .5 read as point five.
6⁄10 (six-tenth) = .6 read as point six.
7⁄10 (seven-tenth) = .7 read as point seven.
8⁄10 (eight-tenth) = .8 read as point eight.
9⁄10 (nine-tenth) = .9 read as point nine.

Hundredths

The fractions with 100 as denominator are called hundredths.

We know
100 centi metres (cm) = 1 metre (m)
or 1 cm = 1⁄100 m or one-hundredth m ;
or 73 cm = 73⁄100 m or seventy three-hundredth m

100 cents = 1 dollar
or 1 cent = 1⁄100 dollar ; or 37 cents = 37⁄100 dollar

We denote hundredths by two digits after the point

We write the fractional number 1⁄100 (one-hundredth)
as .01 read as decimal zero one or point zero one.

Similarly, we write the fractional number 2⁄100 (two-hundredth)
as .02 read as point zero two.

Like wise,
23⁄100 (twenty three-hundredth) = .23 read as point two three.
54⁄100 (fifty four-hundredth) = .54 read as point five four.
35⁄100 (thirty five-hundredth) = .35 read as point three five.
96⁄100 (ninety six-hundredth) = .96 read as point nine six.
47⁄100 (forty seven-hundredth) = .47 read as point four seven.
88⁄100 (eighty eight-hundredth) = .88 read as point eight eight.
19⁄100 (nineteen-hundredth) = .19 read as point one nine.

Thousandths

The fractions with 1000 as denominator are called thousandths.

We know
1000 metres (m) = 1 kilo metre (km)
or 1 m = 1⁄1000 km or one-thousandth km ;
or 573 m = 573⁄1000 km or Five hundred seventy three-thousandth km

1000 grams (g) = 1 kilo gram (kg)
or 1 g = 1⁄1000 kg ; or 337 g = 337⁄1000 kg

We denote thousandths by three digits after the point

We write the fractional number 1⁄1000 (one-thousandth)
as .001 read as decimal zero zero one or point zero zero one.

Similarly, we write the fractional number 2⁄1000 (two-thousandth)
as .002 read as point zero zero two.

Like wise,
923⁄1000 (923 thousandth) = .923 read as point nine two three.
854⁄1000 (854 thousandth) = .854 read as point eight five four.
35⁄1000 (35 thousandth) = .035 read as point zero three five.
696⁄1000 (696 thousandth) = .696 read as point six nine six.
47⁄1000 (47 thousandth) = .047 read as point zero four seven.
488⁄1000 (488 thousandth) = .488 read as point four eight eight.
19⁄1000 (19 thousandth) = .019 read as point zero one nine.

The idea of tenths, hundredths, thousandths can be
extended to ten thousandths, hundred thousandths
(lakhths), millionths (ten lakhths) etc.





Tenths, Hundredths, Thousandths with Whole Number

So far what we have seen are less than one.

Consider the mixed fractions
3  110,8  81100,98  7631000.

With the knowledge of Mixed fractions
and what we have learnt so far, we can write
3  110= 3 + 1⁄10 = 3 + .1 = 3.1
8  81100= 8 + 81⁄100 = 8 + .81 = 8.81
98  7631000= 98 + 763⁄1000 = 98 + .763 = 98.763

The idea of tenths, hundredths, thousandths with
whole numbers can be extended to ten thousandths,
hundred thousandths (lakhths), millionths (ten lakhths) etc.with whole numbers.













Decimals

This form (point form) of writing the
tenths, hundredths, thousandths can be extended
to ten thousandths, hundred thousandths (lakhths),
millionths (ten lakhths) etc. and is
called decimal form and the numbers written in
this form are called Decimal numbers
or simply Decimals.

A Decimal has two parts : Whole Number part and Decimal part.
The two parts are seperated by a dot (.), called decimal point.
The Whole Number part is to the left of the point
and the Decimal part is to its right.

For example, in 98.763, we have :
Whole Number part = 98 and Decimal part = .763

The absence of any of these parts
indicate that the part is 0.

For example,
.79 can be written as 0.79 and 32 can be written as 32.0

Exercise

Write as decimals

  1. 3 tenths
  2. 14 hundredths
  3. 5⁄10
  4. 18⁄100
  5. 127⁄1000
  6. 9871⁄10000
  7. 7  210
  8. 1  99100
  9. 9  11000
  10. 29  37100000

For Answers see at the bottom of the page.

Extension of Place value chart of numbers

for study of this go to

Place Value Chart.

Conversion of Fractions to decimals and vice versa

for study of this go to

conversion to Fractions

and

conversion from Fractions

Comparing

for study of this go to

Comparing

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Four fundamental Operations

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Adding,

Subtracting,

Multiplying

and

Dividing

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Answers to Exercise

  1. 0.3
  2. 0.14
  3. 0.5
  4. 0.18
  5. 0.127
  6. 0.9871
  7. 7.2
  8. 1.99
  9. 9.001
  10. 29.00037