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GENERAL MATH INSTRUCTIONS
Decimals
1. When adding decimals…
a. Line up problem so decimals are in a line
b. Add zeros to the end of a number if necessary
c. EX: 123 + 0.0079 + 43.5 = ? should be written…
123.0000
0.0079
+ 43.5000
166.5079
d. Practice:
1. 136.04 + 102.27 = _________
2. 225 + 15.547 = ___________
Answers: 1) 238.31 2) 240.547
2. When subtracting decimals…
a. Line up problem so decimals are in a line
b. Add zeros to the beginning or end of number if necessary
c. EX: 27.583 – 0.2 = ? should be written…
27.583
-00.200
27.383
d. Practice:
1. 2.37 – 0.031 = _______________
2. 23.1 – 5.51 = _______________
Answers: 1) 2.339
2) 17.59
3. When multiplying decimals…
a. Set the problem up as normal. Do not worry about lining decimal points up.
b. Multiply as usual.
c. Count up the number of “hops” or decimal movements for each number and use that for placement
of decimal in answer.
d. EX: 1.124 x 1.5 = ? should be written…
1.124  # of decimal places = 3
x 1.5  # of decimal places = 1
5620
total decimal places = 4
11240
16860
Since there are 4 decimal places total in the problem, you move the decimal 4 places in the
answer so the answer is 1.6860
e. Practice:
1. 5.4 x 0.05 = ______________
2. 34.56 x 4.8 = ________________
3. 1.592 x 0.011 = _______________
Answers: 1) 0.27
2) 165.888
3) 0.017512
4. When dividing decimals…
a. Make the divisor a whole number by moving the decimal point to the right until you “get rid” of the
decimal.
b. Move the decimal point in the dividend by the same number of places.
c. Place the decimal point in the answer lined up with decimal point in the dividend
d. Divide the numbers. Be sure that the decimal points remain lined up.
e. EX: 12.64 ÷ 0.2 = ? should be written…
0.2 12.64
.
2.0 126.4
2.0
63.2
126.4
f. Practice:
1. 0.24 ÷ 0.08 = ___________
2. 643.2 ÷ 6.7 = ____________
3. 8.36 ÷ 1.9 = ____________
Answers: 1) 3.0
2) 96.0
3) 4.4
Scientific Notation
1. When adding or subtracting in SN…
a. When adding or subtracting in SN, you must express the numbers as the same power of 10.
b. Change the decimal place of the smaller coefficient so the exponents are the same as the larger one.
c. Add or subtract the coefficients as usual.
d. EX: 3.76 x 104 + 5.5 x 102
3.76 x 104 + 0.055 x 104 = 3.815 x 104
e. Practice:
1. (3.95 x 105) + (7.8 x 103)
2. (6.423 x 101) + (5.001 x 10-1)
3. (7.83 x 10-2) - (2.20 x 10-3)
4. (4.54 x 107) - (1.01 x 108)
Answers: 1) 4.028 x 105
2) 6.47301 x 101
3) -7.61 x 102
6) -5.56 x 107
2. When multiplying in SN…
a. When you multiply numbers with SN, multiply the coefficients together and ADD the exponents.
The base will remain 10.
b. EX: (2.87 x 105) x (3.514 x 109)
Part 1: Multiple the coefficients together using decimal rules.
3.514
x 2.87
24598
281120
+702800
1008518
There are 5 decimal places in original question so the answer to the first part is 10.08518
Part 2: Add the exponents
5 + 9 = 14
Answer: 10.08518 x 1014 (or to make it more accurate, move decimal to the left one more place to
have 1.008518 x 1015) Remember, your first number should not be
greater than 9.
c. Practice:
1. (6.8 x 103) x (4.54 x 106)
2. (5.0 x 10-2) x (7.85 x 104)
3. (2.21 x 105) x (1.807 x 10-7)
Answers: 1) 3.1 x 1010
2) 3.9 x 103
3) 3.99 x 10-2
3. When dividing in SN…
a. When dividing in SN, divide the coefficients and SUBTRACT the exponents. The base will remain
10.
b. EX: (9.2 x 10-3) ÷ (6.3 x 106)
Part 1: Divide coefficients
6.3 9.20
.
63 92.0
63
move decimal to the right to get rid of decimal. Do the same for both numbers.
carry the decimal point up above the bracket
1.46
92.0
Part 2: Subtract exponents
-3 – 6 = -9
Remember… -3 – 6 is the same as -3 + -6 = -9
Answer: 1.46 x 10-9
c. Practice: Don’t forget to move your decimals and change your exponents if your coefficient is
greater than 9!
1. (1.92 x 10-2) ÷ (2.3 x 106)
2. (2.4 x 106) ÷ (5.49 x 10-9)
3. (9.4 x 102) ÷ (1.24 x 10-5)
Answers: 1) 8.3 x 10-9
2) 4.4 x 1014
3)7.6 x 107