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Decimals on a Number Line

Introduction

Decimal number is a number which always uses 10 as its base and it is most widely used to solve the complex problems. It is denoted with a dot (.) in between it. Decimal numbers do not necessarily contain a decimal point; 563, 5.63, and -563 are all decimal numbers.

Example:

The decimals 0.7, 0.64, and 0.037 can be expressed as the decimal fractions 7/10, 64/100, and 37/1,000. They are all terminating decimals. These fractions can equally be expressed as the percentages 30%, 51%, and 2.3%.

Number Line Notation

A line is infinite in character.that means all whole numbers may be noted on a number line.The least whole number is zero.the highest whole number cannot be stated as the set of whole numbers is infinite.

Properties of Whole Numbers

It is advisable to use a number line in-order to understand the properties of whole numbers.

1. There is no whole number to the left of zero on the number line.So zero is the smaller number than each of the numbers to its right on the number line.That means 0 is the smallest or least of the whole numbers.

2. A whole number which is greater than a given whole number by 1 is said to be a successive whole number. 1 is the successive whole number to 0.Every whole number has one successor.

3. There is no whole number left to zero.hence 0 is not a successive whole number of any whole.

Positions of Decimal Numbers

The unit places of any decimal number are denoted by using positions tenths place, hundredths place, thousands place etc.

Tenths place, Hundredths place and Thousandths place:

Tenth Place

• The tenths place in any decimal number lies immediately after dot (.) Tenths place can be determined by making 10 parts between any two consequent numbers.

Example:

Take the number 0 and 1 and make it into 10 parts such that we can represent it as

0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0

And its number line is determined as:

Decimals On A Number Line

Hundred Place

• The hundredths place in any decimal number lies immediately after tenths place; hundredths place can be determined by making 100 parts between any two consequent numbers.

Example:

Take the number 0 and 1 and make it into 100 parts such that we can represent it as

0.00,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.10,0.11…………………………1.00

And its number line is determined as:

Decimals On A Number Line

Thoshand Place

• The thousands place in any decimal number lies immediately after hundredths place; thousands place can be determined by making 1000 parts between any two consequent numbers.

Example:

Take the number 0 and 1 and make it into 1000 parts such that we can represent it as

0.000,0.001,0.002,0.003,0.004,0.005,0.006,0.007,0.008,0.009,0.010,0.011…………………………1.000

And its number line is determined as:

Decimals On A Number Line

Usually we get a decimal number by multiplying any number with 10-1 or 1/10. Similarly to get a hundredths we use 10-2 or 1/100 and 10-3 or 1/1000 etc.

So here in decimal number line tenths number is greater than the hundredths and thousandths number.

Write the Decimal Form in Different Notation

0.5>0.05>0.05>0.005>0.0005>………………………..>0.000000000000000..05

Given:

The decimal form can be changed to 10 power based on decimal position:

5x10-1>5x10-2>5x10-3>5x10-4>……………………………..>5x10-?

Put the Following Decimal Numbers in Ascending Order

0.4, 0.1, 0.5, 0.7, 0.6

Given:

Change the decimals into ascending order ie incerasing order:

0.7>0.6>0.5>0.4>0.1

Put the Following Decimal Numbers in Descending Order

0.4, 0.1, 0.5, 0.7, 0.6

Given:

Change the decimals into descending order ie decreasing order:

0.1>0.4>0.5>0.6>0.7