Scaling & Types Of Decimals

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Unit: Number System

Chapter: Scaling & Types of Decimals

Reference: – Introduction to Scaling in Decimals, Multiplying and Dividing Decimals by Powers of 10, Shifting the Decimal Point, Scaling Up and Scaling Down Decimals, Types of Decimals (Terminating, Recurring/Non-Terminating Repeating, Non-Terminating Non-Recurring), Like and Unlike Decimals, Converting Between Decimal Types

After studying this chapter, you should be able to understand:

Introduction to Scaling in Decimals
Multiplying Decimals by Powers of 10 (Scaling Up)
Dividing Decimals by Powers of 10 (Scaling Down)
Shifting the Decimal Point
Types of Decimals (Terminating, Recurring, Non-Terminating Non-Recurring)
Like and Unlike Decimals
Converting Between Decimal Types

Conversion of Decimal into a Fraction

To convert decimals into fractions, we will divide the decimal number by the 10, 100, 1000, etc. depending upon the number of figures after decimal point. In simple words, we have to divide the decimal numbers by the total number of decimal places to right.

Let us look at the steps to be followed for converting a decimal to a fraction-

Step 1 : Write the given number without decimal point as the numerator of the fraction.

Step 2 : In the denominator, write 1 followed by as many zeros as there are decimal places in the given number

Step 3 : Reduce the fraction to the lowest term.

Example :

1. Convert each of the following into fractions.

(i) 3.63

Solution:

3.63

= 3.63 × 100100

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= 363100

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(ii) 2.023

Solution:

2.023

= 2.023 × 10001000

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= 20231000

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Conversion of Fraction into Decimal

Converting fractions with denominator as 10, 100, 1000, etc..

We count the number of zeroes in the denominator.
Starting from right we count the number of places towards the left in the numerator as equal to the number of zeroes in the denominator and put a decimal point after that.

Examples-

310

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= 0.3

Since, there is 1 zero in the denominator we put a decimal point after 1 place towards left counting from 3.

119100

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= 1.19

Since, there are 2 zeroes in the denominator we put a decimal point after 2 places towards left counting from 9.

Converting fractions whose denominator can be converted to equivalent of 10, 100, 1000, etc..

We convert the fraction to its equivalent such that the new denominator is either of 10, 100, 1000, etc

Then, starting from right we count the number of places towards the left in the numerator as equal to the number of zeroes in the denominator and put a decimal point after that.

Examples-