The document defines several key mathematical concepts: - Additive identity is the value of 0, as adding 0 to any number yields the original number. - Multiplicative identity is the value of 1, as multiplying any number by 1 yields the original number. - An additive inverse of a number x is -x, as x + (-x) = 0. - A multiplicative inverse or reciprocal of a number x is 1/x. - Decimals represent fractions in base-10, with the 10th, 100th, 1000th parts called tenths, hundredths, thousandths and so on.

1. ADDITIVE IDENTITY
• ADDITIVE IDENTITY IS THE VALUE WHEN ADDED TO A NUMBER, RESULTS IN THE ORIGINAL NUMBER.
• WHEN WE ADD 0 TO ANY REAL NUMBER, WE GET THE SAME REAL NUMBER.
• FOR EXAMPLE, 5 + 0 = 5. THEREFORE, 0 IS THE ADDITIVE IDENTITY OFANY REAL NUMBER.

2. MULTIPLICATIVE IDENTITY
•MULTIPLICATIVE IDENTITY PROPERTY SAYS
THAT WHENEVER A NUMBER IS MULTIPLIED BY
THE NUMBER 1 (ONE) IT WILL GIVE THAT
NUMBER AS A PRODUCT. “

3. ADDITIVE INVERSE
•ADDITIVE INVERSE SIMPLY MEANS CHANGING THE SIGN OF THE
NUMBER AND ADDING IT TO THE ORIGINAL NUMBER TO GET AN
ANSWER EQUAL TO 0.
•FOR EXAMPLE, X IS THE ORIGINAL NUMBER, THEN ITS ADDITIVE
INVERSE IS -X.

4. MULTIPLICATIVE INVERSE
•A MULTIPLICATIVE INVERSE OR
RECIPROCAL FOR A NUMBER X,
DENOTED BY 1/X

5. DECIMALS
•10TH,100TH ,1000TH & NTH PART OF ANY
FRACTION IS CALLED DECIMALS.
•FOR EXAMPLE:
•0.1 ,0.01, 0.001,……..

6. TYPES OF DECIMALS
•TERMINATING
•A FRACTION THAT HAVE DECIMALS PART AND COMPLETELY
DIVIDED IS CALLED TERMINATING.
•FOR EXAMPLE: 22.345,0.25,1.2 ETC.
•NON TERMINATING
•A FRACTION THAT HAVE DECIMALS PART AND NOT COMPLETELY
DIVIDED IS CALLED TERMINATING.
•FOR EXAMPLE: 22.345……,0.25……,1.2…… ETC.

7. TYPES OF NON TERMINATING
•RECURRING/REPEATING
•A NON TERMINATING DECIMAL HAVING SAME(REPEATING) ELEMENTS IN ITS
DECIMAL PART IS CALLED RECURRING/REPEATING
•E.G: 1.6666….,23.545454….,0.123123123….,ETC
•NON RECURRING/ NON REPEATING
•A NON TERMINATING DECIMAL HAVING DIFFERENT(NON REPEATING)
ELEMENTS IN ITS DECIMAL PART IS CALLED NON RECURRING/ NON
REPEATING. E.G: 1.64536….,23.45214….,0.231312….,ETC

8. WITHOUT DIVIDING YOU CAN TELL FARACTION TYPE
FOR TERMINATING DECIMALS, FACTORS OF DENOMINATOR SHOULD BE IN THE FORM OF 2M×5N.
• (I) 1380
• HERE, DENOMINATOR IS 80 80=2×2×2×2×5=24×5
• HENCE DENOMINATOR DOESN'T HAVE ANY FACTOR OTHER THAN 2 OR 5.
• SO, THE NUMBER IS TERMINATING.
• (II) 724
• DENOMINATOR IS 24.
24=2×2×2×3=23×3
Hence, denominator has factor other than 2 or 5.
So, the number is non-terminating.

9. WITHOUT DIVIDING YOU CAN TELL FARACTION TYPE
(iii) 512
Denominator is 12.
12=2×2×3=22×3
Hence, denominator has factor other than 2 or 5.
So, the number is non-terminating.

10. WITHOUT DIVIDING YOU CAN TELL FARACTION TYPE
• (IV) 31375
• DENOMINATOR IS 375.
• 375=5×5×5×3=53×3
• HENCE, DENOMINATOR HAS FACTOR OTHER THAN 2 OR 5.
• SO, THE NUMBER IS NON-TERMINATING.
• (V) 16125
• DENOMINATOR IS 125.
• 125=5×5×5=53
• HENCE, THE DENOMINATOR DOESN'T HAVE ANY FACTOR OTHER THAN 2 OR 5.
• SO, THE NUMBER IS TERMINATING.

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