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# Math Reviewer

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Name : ______________________________________ Lesson 1 : Place Value

The 'zeroth power' of any number always equals one
Ex.
3 = 1. 1994587685775 = 1. 8999 = 1. 92 = 1.

The exponent equals the number of DECIMAL PLACES.
7
Ex.
Exponent 7 = 7 places
1 2 3 4 5 6 7
10 = 10 000 000
1 x 10 = 1
10 = 10
10 = 100
10 = 1 000
10 = 10 000
10 = 100 000

-5
10 = 0.000 01

10 -1 = 0.1
10 -2 = 0.01 1 2 3 4 5
10 -3 = 0.001
Exponent -5 = 5 DECIMAL places INCLUDING 1
10 -4 = 0.0001
10 -5 = 0.00001

5. 27 x 101 = _______________ 6. 128 x 108 = _______________ 7. 77 x 10 -6 = _______________ 8. 122 x 10 - 9 = ______________

9. 10.

EXERCISE: PLACE VALUE 1. 2 x 101 = _______________ 2. 4 x 107 = _______________ 3. 9 x 10 - 5 = ______________ 4. 8 x 10 - 10 = _____________

Write in standard form:
1. seven hundred seventy seven an three hundred sixty eight thousandths _________________
2. ninety two thousand and two hundred one ten thousandths ______________________
3. five hundred eighty eight millionths ____________________________

Give the place value of the digit 7 in each number
1. 6.123457 ____________________________ 2. 9457.2234 _____________________
3. 3.2355622547 ______________________________ 4. 712.4532 _______________________

Give the value of each underlined digit
1. 0.234571 __________________________ 2. 93858.478432 _______________________
3. 0.297175762 ________________________ 4. 267385256781_______________________

Write the number in standard form
1. six and four hundred thousandths ________________________________
2. four hundred forty four and two hundred one millionths_________________________________
3. (3 x 105) + (2 x 107) = (3 x 105) + (200 x 105) = _______________________________________
4. (2 x 104) + (9 x 10-7) = (1 x 106) + (200 x 10-5) = _______________________________________

Write as an addition expression in exponential form
1. 77.901605 =___________________________________________________________________
Write the decimal number for each expression :
1. 2100 + 14100 +17 + 510000 = _______________ 2. 459910000 = _______________

Lesson 2 : Fractions and Decimals
Nonterminating = repeating
Change NONTERMINATING DEIMAL decimal to fraction :
0.312 = 312 x 1(1000-1) = 312 x 1999 = 312999 or 104333
0.23 = 23 x 1(100-1) = 23 x 199 = 2399 0.7 = 7 x 1(10-1) = 7 x 19
LOWEST term!! = 79

Give the decimal equivalent :
1. 2212 ___________ 2. 513 ___________ 3. 1517 ____________ 4. 206 ____________

Lesson 3 : Comparing Decimals
Write > , < or = 4.7 ____ 4.071.6 ____ 6.12.98 ____ 3.01 | 3.06____ 3.6085.58 ____ 58.855.45 ____5.405 | 1.600 _____ 1.685.51 _____ 83.3144.044 _____ 44.404 |
Arrange from least to greatest
A. 6.5 , 5.069 , 9.05 , 5.906 , 5.6 ___________________________________________________________
B. 23.056 , 32.506 , 23.650 , 23.56 , 32.6 ____________________________________________________________
C. 17.509, 17.905 , 8.99 , 17.99 , 17.099 _____________________________________________________________

Arrange from greatest to least
A.. 0.01 , 0.1 , 1.0 , 1.01 ________________________________________________________________
B . 0.00002 , 0.2 , 0.009 , 0.9 , 0.9999 ________________________________________________________
Lesson 4 : Rounding Off
Round off :
143 568 984 . 940 108 463

nearest ones ≈ _____________________________________________ nearest tens ≈ ____________________________________________ nearest hundreds ≈ _____________________________________________ nearest thousands ≈ _____________________________________________ nearest hundred thousands ≈ _____________________________________________ nearest millions ≈ _____________________________________________ nearest billions ≈ _____________________________________________ nearest tenths ≈ _____________________________________________ nearest hundredths ≈ _____________________________________________ nearest thousandths ≈ _____________________________________________ nearest ten thousandths ≈ _____________________________________________ nearest hundred thousandths ≈ _____________________________________________ nearest millionths ≈ _____________________________________________ nearest ten millionths ≈ _____________________________________________

Lesson 5 : Addition and Subtraction of Decimals
Rule # 1 : Always ALIGN the DECIMAL POINT
Solutions :
Rule # 2 : Always follow rule no. 1

Perform indicated operations :
1. 0.938562 – 0.0382 = _________________________
2. 12.00245 + 0.39545 = ________________________

Lesson 6 : Multiplication Decimals
Multiply :
Solution :
Solution :
1. 12.345 x 543.21 = ______________________ 2. 1345.34 x 0.0004 = _________________________

Lesson 6 : Division Decimals

Divide :
Solution :
Solution :

1. 2. 13.445 ÷ 0.15

Lesson 7 : Ratio and Rate 3 : 4 = 34
Division or simplifying only
Simplify in ratio or as a unit rate
1. 10 minutes to 1 hour ________________ 2. 2 years to 4 months __________________
3. 10 000 miles in 60 seconds ____________ 4. 15 bags in 165 minutes ________________
5. 4 weeks to 4 days __________________ 6. 35 : 710 ___________________
7. 54 : 912 ____________________
Lesson 8 : Proportion
5 15
- = -- x 12

Find missing : 1 x - = - 2 6 x = ________ x = ________ x = ________

Lesson 9 : Positive Negative Integers
1. 20 units up _________
2. 50 units down __________
3. A loss of 55 pesos __________
4. an income of 5000 pesos _______

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