1. Math 009
Unit 4
Lesson 1

2. Obj: To write decimals in words
thousandths
ten-thousandths
and
tenths
hundredths
ones
hundreds
tens 1 5 1 5 7
15.157
Fifteen and one hundred fifty-seven thousandths

3. Obj: To write decimals in words
thousandths
ten-thousandths
and
tenths
hundredths
ones
hundreds
tens 3 6 1 7
Three hundred six and seventeen ten-thousandths

4. Obj: To write words as decimals
thousandths
ten-thousandths
and
tenths
hundredths
ones
hundreds
tens 5 3 8
Five and thirty-eight hundredths
Answer:
5.38

5. Obj: To write words as decimals
thousandths
ten-thousandths
and
tenths
hundredths
ones
hundreds
tens 1 9 4
Nineteen and four thousandths
Answer:
19.004

6. Obj: To write words as decimals
thousandths
ten-thousandths
and
tenths
hundredths
ones
hundreds
tens 7 1
Seventy-one ten-thousandths
Answer:
0.0071

7. Naming place values: Name the place value of the digit 7 56.03789
thousandths
hundred-thousandths
tenths

8. Ordering decimal numbers
Place the correct symbol between the two numbers
Line up the decimals
<
7.6005
7.605
Write the following numbers in order from smallest to largest
0.24, 0.024, 0.204,
0.24
0.024
0.204
0.0024
0.024
0.0024
Answer:
0.24
0.204
0.0024, 0.024,
0.204, 0.24

9. Obj: To round a decimal to a given place value.
Round to the nearest hundredth
4.35
Round to the nearest ten-thousandth
4.3493

10. Obj: To round a decimal to a given place value.
Round to the nearest tenth
4.3
Round to the nearest hundredth
15.05
Round to the nearest tenth
15.1

11. Operations on decimals

12. Obj: To add decimals without a calculator
Write the numbers so that the decimals points are on a vertical line
add the columns just as you would with whole numbers
Example: Find the sum of 42.3, and 1 1 1 + 9
0.2759
.2759
759 59
Answer:

13. Obj: To subtract decimals without a calculator
Write the numbers so that the decimals points are on a vertical line
subtract the columns just as you would with whole numbers
Example: Subtract and 7.96 14 8 9
39.047 –
7.96
Answer:

14. Find the following sums or differences =
– (-8.3) =
= 9.39
– (-3.82) –
= – =
4. How much greater is -31 than ?
-31 – (-62.09) = =

15. Obj: To solve application problems involving decimals
Find the missing length on the shaft
8.6 cm
2.77 cm ?
3.2 cm
Solution:
= 5.97
missing length = 8.6 – 5.97
missing length = 2.63 cm

16. Obj: To solve application problems involving decimals
Grace owned shares of a mutual fund on January 1. On December 31 of the same year she noticed that her shares had increased by shares. What was her new total at the end of that year?
Solution:
New Total =
= shares

17. Estimate by rounding; then find the exact answer
6.272 – 1.848
Estimation:
6 – 2 = 4
Exact answer:
6.272 – =
Evaluate x – y when x = and y =
x – y =
6.029 – (-4.708) = =

18. Obj: To multiply decimals without a calculator
multiply the numbers as if they were whole numbers
the number of decimal places in the answer is the sum of the decimal places in the factors
Multiply: x
Total decimal places in the factors is 9 x
602
430
Total decimal places in the answer is 9
00000
4902 ^
Answer:

19. Obj: To divide decimals without a calculator
Round your answer to the nearest tenth 5 9 6 1
7.06
420.9
706
42090. 00 ^ ^
3530
Answer
59.6
679
6354
436
423 6
12 4
7 06

20. Do the following multiplications and divisions
(0.72)(-3.7)
-5.2(-0.8)
(10,000)
¸ (-0.4)
58.37 ¸ 1000 = = = = =

21. Do the following multiplications and divisions
Round answers to the nearest hundredth
(5.78)(-3.799)
-(18.47)(2.003)
8.57 ¸
¸ (-3.14) = » = » = » = »

22. Obj: To multiply decimals by powers of 10
move the decimal point to the right the same number of places as the number of zeros in the power of 10
Multiply: x 1000
.4207 x 1000
= 4207 = ^
Multiply: x 10,000
63.75 x 10,000
= 6375 00
= 637,500 ^

23. Obj: To multiply decimals by powers of 10
if the power of 10 is written in exponent form
move the decimal point to the right the same number of places as the power of 10
Multiply: x 103
x 103 = = ^
Multiply: x 105
4.68 x 105
= 468
000
= 468,000 ^

24. Obj: To divide decimals by powers of 10
move the decimal in the dividend to the left the same number of places as the power of 10 (same number of places as the number of zeros)
Divide: ¸ 103
58.3 ¸ 103 = = ^
Divide: ¸ 100
0.625 ¸ 100 = = ^

25. 8 4 8. 68 4. 1666… 4.16 Obj: To convert fractions to decimals
divide the numerator by the denominator
place a bar over repeating digits
round the decimal answer if necessary
Convert to a decimal:
3 8 =
0.375
17 25 8 8. 68 =
1 6 4 4.
1666…
4.16 = =

26. Certain conversions from fractions to decimals should be memorized
Obj: To convert fractions to decimals
Certain conversions from fractions to decimals should be memorized 14 =
0.25 13 =
0.333… = 0.3 12 =
0.5 23 =
0.666… = 0.6 34 =
0.75

27. 5 5 Obj: Convert decimals to fractions Convert fractions 35 7 = 0.35 =
remove the decimal point
for a denominator use a power of ten that corresponds to the decimal places in the original number
reduce the fraction
Convert fractions 35 7 =
0.35 =
100 20
275 11 =
0.275 =
1000 40 5 5
19 25
5.76 = =

28. > < Obj: Compare a decimal and a fraction 3 8 4.509 4 0.32 0.32
change the fraction to a decimal
compare the decimals
Place the correct symbol, > or <, between the numbers
3 8
> 12
<
4.509 4
0.32
0.32
0.375
4.509
4.5
0.32
4.509
0.375
4.5 00

29. Checking a solution to an equation
Is a solution for 6.4 = x ?
6.4 = x
6.4
5.2 + (-1.2) 4
No , is not a solution for the equation

30. Checking a solution to an equation
Is a solution for -9x = ?
-9x =
-9(-3.6)
32.4
32.4
Yes , is a solution for the equation