Basic Math Skills Review

1. Basic Math Skills Review Decimals

2. Introduction to Decimals • Numbers to the right of a decimal point are less than one. • The decimal place is the number of digits to the right of the decimal point. • As the number of decimal places increases, the value of the number gets smaller. • Whole numbers can be written with a decimal point to the right of the ones place followed by zeros. • Zeros are place holders between non-zero numbers. • Decimals can be converted to exponents or fractions.

3. Place Value The suffix “–ths” indicates that the digits are to the right of the decimal point. The decimal point replaces the ones place.

4. Converting Fractions to Decimals In order to write a fraction as a decimal, you must have a power of ten in the denominator. The number of zeros in the denominator is equal to the number of decimal places. If the denominator is not a power of ten you must either: 1) Find an equivalent fraction or 2) Divide and write the quotient in decimal form.

5. Powers of Ten 103 102 101 100 10-1 10-2 1000 100 10 1 Brief review of exponents: 102=100 102=10•10=100 base power exponent

6. Example: Equivalent Fractions There are some fractions which can be easily converted to decimals. An example of this are ones with factors of 100 in the denominator. Look for: 2, 4, 5, 10, 20, 25, 50

7. Example: Equivalent Fractions Since the equivalent fraction has two zeros in the denominator, we can rewrite it as a number with two decimal places. It even works with improper fractions.

8. Example: Equivalent Fractions There are some fractions which can be easily converted to decimals. Another example of this are ones with factors of 10 in the denominator. Look for: 2 or 5 Since the denominator is a 10, there is only one decimal place.

9. Addition 1) Line up the decimal points. 2) Write zeros at the right end of the numbers, if needed. 3) Find the sum (just like with whole numbers). 4) Bring down the decimal point.

10. Example: Addition Note: Decimal points are written to the right of the ones place in whole numbers. Re-write before solving Line up decimal points and add

11. Subtraction 1) Line up the decimal points. 2) Write zeros at the right end of the numbers, if needed. 3) Find the difference (just like with whole numbers). 4) Bring down the decimal point.

12. Example: Subtraction Line up the decimal points. Write zeros at the right end of the numbers, if needed. Find the difference Bring down the decimal point

13. Multiplication 1) Find the product (just like whole numbers). 2) Count the number of decimal places in the factors. 3) Start at the ones place in the product. Count the digits (from right to left) the number of places from step 2. Place the decimal point to the left of the digit you stopped on.

14. Example: Multiplication Find the product Count the number of decimal places in the factors. In this example, there are three decimal places. Move the decimal three place to the left. The final answer is 13.608

15. Division Only use these rules if there is a decimal in the divisor. If not, move the decimal directly up to the top of the division symbol and divide. 1) Move the decimal point as many places to the right as needed to make the divisor a whole number. 2) Move the decimal of the dividend the same number of places. Annex zeros, if needed. 3) Move the decimal point to the top of the long division symbol ( ). 4) Find the quotient.

16. Example: Division Find the quotient of 4.8 by 2.4. Set up the problem: Move the decimal point to make the divisor a whole number. 1 decimal place Move the decimal of the dividend the same number of places. 1 decimal place Move the decimal point to the top of the division symbol. Find the quotient.

17. NOVA Math Placement Test • The Math Placement test is given in the Testing Center. • There is a review book for the placement exam in the Annandale Library. (CG 3rd Floor) • It’s called Chart Your Success on the Compass Exam. • Brush-up on current skills, go through what you know. • Don’t try to teach yourself anything that you do not know. • Use the list of suggested websites to help you review. • Neither the Math Center nor the Tutoring Center will help you study for the exam.