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.
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Additive identity.pptx
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.
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.
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.