1. Chapter R
Prealgebra Review
Decimal Notation

2. R.3
DECIMAL NOTATION
a. Convert from decimal notation to fraction notation.
b. Add, subtract, multiply, and divide using decimal notation.
c. Round numbers to a specified decimal place.

3. The decimal notation 42.3245 means
The decimal notation means
4 tens + 2 ones + 3 tenths + 2 hundredths + 4 thousandths + 5 ten-thousandths
We read this number as:
“Forty-two and three thousand two hundred forty-five ten-thousandths.”
The decimal point is read as “and”.

4. To convert from decimal to fraction notation:
a) Count the number of decimal
places.
b) Move the decimal point that
many places to the right.
c) Write the result over a
denominator with that number
of zeros.
To convert from decimal to fraction notation:
4.98
2 places
4.98
Move
2 places.
2 zeros

5. Write fraction notation for 0.924. Do not simplify. Solution 0.924

6. Write fraction notation for 0.924. Do not simplify. Solution 0.924
3 zeros
3 places

7. Write 17. 77 as a fraction and as a mixed numeral
Write as a fraction and as a mixed numeral. Solution To write as a fraction: 17.77
2 zeros
2 places
17.77.
To write as a mixed numeral, we rewrite the whole number part and express the rest in fraction form:

8. a) Count the number of zeros.
b) Move the decimal point that
number of places to the left. Leave
off the denominator.
To convert from fraction notation to decimal notation when the denominator is 10, 100, 1000 and so on,
3 zeros
8.679.
Move
3 places.

9. Write decimal notation for Solution
1 zero
1 place

10. Adding with decimal notation is similar to adding whole numbers.
First we line up the decimal points in addition so that we can add corresponding place-value digits.
Add the digits from the right.
If necessary, we can write extra zeros to the far right of the decimal point so that the number of places is the same.
Place the decimal point in the answer in line with decimal points in numbers.

11. Add: 4.31 + 0.146 + 14.2 Subtract: 34.07 – 4.0052 Subtract 574 – 3.825

12. Add:
Solution: Line up the decimal points and write extra zeros. 1 8 . 6 5 6

13. Subtract: – Solution Line up decimal points and subtract, borrowing if necessary – 6 9 10 3 . 6 4 8

14. Subtract 574 – Solution – 3 9 9 10 5 7 . 1 7 5

15. a) Ignore the decimal points, and multiply as whole numbers.
b) Place the decimal point in the result of step (a) by adding the number of decimal places in the original factors.
Multiplication with Decimal Notation

16. Multiply 7.3  85.1.

17. Multiply 7.3  85.1.
Solution
Ignore the decimal points and multiply as if both factors are integers then place the decimal point.  3
1 decimal place 1
1 decimal place .
2 decimal places

18. b) Divide as whole numbers.
a) Place the decimal point in the quotient directly above the decimal point in the dividend.
b) Divide as whole numbers.
Dividing When the Divisor is a Whole Number

19. Divide  26.

20. Divide  26. Solution
place the decimal point

21. b) Divide as whole numbers, inserting zeros if necessary.
a) Move the decimal point in the divisor as many places to the right as it takes to make it a whole number. Move the decimal point in the dividend the same number of places to the right and place the decimal point in the quotient.
b) Divide as whole numbers, inserting zeros if necessary.
Dividing When the Divisor is Not a Whole Number

22. Divide:  9.6.

23. Divide:  9.6. Solution  9.6 = 0.82.
Move the decimal point in the divisor 1 place to the right. Move the decimal point in the dividend 1 place to the right.

24. Find decimal notation for

25. Find decimal notation for Solution
You might also divide 7 by 25 to get this answer.

26. Find decimal notation for
Solution Divide 1  12
Since 4 keeps reappearing as a remainder, the digit 3 will continue to repeat in the quotient; therefore,
The dots indicate an endless sequence of digits in the quotient. The dots are often replaced by a bar to indicate the repeating part.

27. Find decimal notation for
Solution
5  11
Since 6 and 5 keep reappearing as
remainders, the sequence of digits
“45” repeats in the quotient, and

28. To round to a certain place: a) Locate the digit in that place.
b) Consider the digit to its right.
c) If the digit to the right is 5 or higher, round up, if the digit to the right is less than 5, round down.
Rounding Decimal Notation

29. Round 0. 072 to the nearest tenth. Round 34
Round to the nearest tenth. Round to the nearest hundredth. Round to the nearest thousandth, hundredth, tenth, ones, tens, hundreds, and thousands.

30. Round 0. 072 to the nearest tenth. Solution a
Round to the nearest tenth. Solution a. Locate the digit in the tenths place b. Consider the next digit to the right. c. Since that digit, 7 is greater than 5, round up: 0.1

31. Round 34. 7824 to the nearest hundredth. Solution a
Round to the nearest hundredth. Solution a. Locate the digit in the hundredths place b. Consider the next digit to the right. c. Since that digit, 2 is less than 5, we round down:

32. Round to the nearest thousandth, hundredth, tenth, ones, tens, hundreds, and thousands. Solution 4 7 8 . 3 6 9
thousandth
hundredth 5
tenth
one
ten
hundred
thousand