1. KU 122 Introduction to Math Skills and Strategies Unit THREE Welcome ~

2. Decimal Notation Decimals…are fractional values that have a denominator with a power of 10; we use it for money; cost of items and various daily operations Terms we will be working with…

3. Decimal Notation 42.3245 The decimal notation 42.3245 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. Decimal Notation Convert between fraction notation and decimal notation This has three decimal places…so three zeros Count the number of spaces after the decimal and that is the number of zeros

5. Decimal Notation Write fraction notation for 0.924. Do not simplify. And we can convert back to fractions as well such as 53/10 is what in decimals? 5.3 since only ONE zero, so one space after decimal

6. Decimal Notation Write this as a decimal notation 134,027 / 10,000

7. Decimal Notation Write this as a decimal notation 134,027 / 10,000 We have 4 zeros in the denominator; means we need 4 spaces after the decimal…. 13.4027

8. Decimal Notation Ok, don’t get tricked…try this one… 11 / 1000

9. Decimal Notation 11 / 1000 There are three zeros in the denominator; means there needs to be three spaces after the decimal 0.011

10. Decimal Notation Adding and subtracting decimals…think of your checkbook! Adding with decimal notation is similar to adding whole numbers. First we line up the decimal points 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.

11. Decimal Notation Lets do this one: 4.31 + 0.146 + 14.2 =

12. Decimal Notation Lets do this one: 4.31 + 0.146 + 14.2 = 04.31 00.146 14.200 ____________ 18.656

13. Lets review now adding a fraction Denominators must be the same to be able to add – check this and convert; then add numerators 3/4 + 2/4 = ? add 3 + 2 = 5 numerator Keep denominator = 5/4 or 1 1/4

14. Decimal Notation Subtracting decimals 34.07 – 4.0052 = Line the numbers up and borrow if you need to; just like normal subtraction

15. Decimal Notation 34.07 – 4.0052 = 34.0700 04.0052 _________ 30.0648

16. Decimal Notation Solve equations of the type x + a = b and a + x = b, where a and b may be in decimal notation. We work this the same way as we did before; get x by itself on one side and solve X + 32.78 = 84.19 lets solve

17. Decimal Notation X + 32.78 = 84.19 lets solve X + 32.78 – 32.78 = 84.19 – 32.78 X + 0 = 51.41 X = 51.41

18. Decimal Notation To multiply using decimals: 0.8  0.43 a) Ignore the decimal points, and multiply as though both factors were whole numbers. b) Then place the decimal point in the result. The number of decimal places in the product is the sum of the number of places in the factors. (count places from the right).

19. Decimal Notation 0.8  0.43 Ignore the decimals and multiply for step one 08 * 043 = 344 Now, add the total number of decimal spaces that were in our equation 0.8 had one space 0.43 had two spaces Therefore we need three spaces in our solution Final answer.344

20. Decimal Notation Try this one….30 *.002 = First ignore the decimals, multiply out and then add up how many spaces each factor had, and this will be how many in your solution

21. Decimal Notation Try this one….30 *.002 = 30 * 002 = 60 Now.30 has two spaces after decimal.002 has three spaces after decimal Add these together; so we need 5 spaces after the decimal Therefore.00006

22. Fractions – lets review how to multiply Do you remember the rules? With Fractions you multiple the numerators across and multiply the denominators across 5/6 * 1/8 5 * 1 (numerators) = 5 6 * 8 (denominators) = 48 5/48 If we wanted to convert to a decimal, what would we do? Divide the numerator into the denominator

23. Decimal Notation To divide when the divisor is not a whole number, a) move the decimal point (multiply by 10, 100, and so on) to make the divisor a whole number, b) move the decimal point (multiply the same way) in the dividend the same number of places, and c) place the decimal point directly above the new decimal point in the dividend and divide as though dividing whole numbers. Example.24 / 8.208 Write out as 24 / 820.8 and divide Final answer 34.2

24. Decimal Notation Now you also need to be able to convert word problems into equations… Let’s try one I had $22.50 to buy fruits and vegetables at the store. I spend $13.12 on vegetables; of which was $3.12 was for potatoes. How much do I have left for fruit? How many lbs of potatoes was I able to purchase if the potatoes cost.12 cents per lb?

25. I had $22.50 to buy fruits and vegetables at the store. I spend $13.12 on vegetables; of which was $3.12 was for potatoes. How much do I have left for fruit? Total to spend is $22.50 Already spent $13.12 How much left for fruit = x $22.50 = 13.12 + x 22.50 – 13.12 = x $9.38 How many lbs of potatoes was I able to purchase if the potatoes cost.12 cents per lb? Potatoes cost $3.12.12 per lb 3.12 /.12 = 26 lbs

26. Q UESTIONS Questions?