Business Math Chapter 3: Decimals

3.1 Decimals and the Place Value System Read and write decimals Round decimals 1.2345 rounded to the nearest tenth is 1.2

3.1.1 Read and write decimals Our money system, based on the dollar, uses the decimal system. Moving one place from right to left increases the value ten times. Moving one place from left to right, causes the value of the digit to become ten times smaller.

How much is 0.1? It is one part of a 10-part whole. 0.1 is read “one tenth” If this chart represented a dollar, the white segment would be equal to $0.10.

The decimal point Separates the whole number part from the decimal part, as the number extends from left to right. 34.7 is read thirty four and seven tenths or 34 point 7.

Place value names The first place to the right of the decimal point is tenths. (0.1) Second place is hundredths. (0.01) Third place is thousandths. (0.001) Fourth place is ten-thousandths. (0.0001) and so on.

How to read or write a decimal 3.12 Three and twelve hundredths 9.067 Nine and sixty-seven thousandths. 4.5 Four and five tenths. Read the whole number part first, saying “and” to indicate the beginning of the decimal part of the number.

Reading decimals as money amounts When reading numbers that represent money amounts, read whole numbers as dollars. Decimal amounts are read as “cents.” $35.98 is read “thirty–five dollars and 98 cents.”

3.1.2 Round to a specific decimal place 1. Find the digit in the specified place. 2. Look at the next digit to the right. If this digit is less than 5, eliminate it and all digits to its right. If the digit is 5 or more, add 1 to the digit in the specified place, and eliminate all digits to its right.

Round to the nearest tenth Try these examples Round to the nearest tenth 12.456 12.5 31,343.387 31,343.4 346.2778 346.3

3.2 Operations with decimals Add and subtract decimals Multiply decimals Divide decimals 3.234 + 6.8 = ?

Add and subtract decimals Write the numbers in a vertical column, aligning digits according to their places. Attach extra zeros to the right end of each number so each number has the same quantity of digits. Add or subtract as though the numbers are whole numbers. Place the decimal point in the sum or difference to align with the decimal point in the respective operation.

Be orderly to avoid mistakes. 3. 4 7 - . 2 9 1 8

Add zeros where necessary .7 8 - .0 9 2 = .6

Try these examples. (Without using your calculator) 7.098 + 2.6 + 0.8 + 13.999 = 24.497 10.008 – 7.6 = 2.408 .976 - .04217 = .93383

3.2.2 Multiply decimals Multiply the decimal numbers as though they are whole numbers. Count the digits in the decimal parts of both decimal numbers. Place the decimal point in the product so that there are as many digits in its decimal part as there are digits you counted in the previous step. If necessary, attach zeros to the left end of the product to place the decimal point accurately.

Look at this example. 3.45 x 4.082 = How many places are there to the right of the decimal point? Five; so, the answer will have five places to the right of the decimal. The answer is 14.08290 The last zero can be dropped and the answer would be 14.0829.

Try these examples (Without using your calculator) 0.144 3.07 x 8.008 = 24.58456 .01 x 1.001= 0.01001

Divide a decimal by a whole number: 3.2.3 Divide decimals Divide a decimal by a whole number: Place a decimal point for the quotient directly above the decimal point in the dividend. Divide as though the decimal points are whole numbers. 3.4 divided by 3 = ?

Try these examples (Without using your calculator) 12.4 ÷ 6 = 2.06 (repeating) 36.5 ÷ 2 = 18.25 192.45 ÷ 50 = 3.849

Try this word problem Jill wants to buy a bottle of detergent. If a 100-ounce bottle costs $6.49 and a 50- ounce bottle costs $3.99, which would be the better buy on cost per ounce basis? What are those amounts? Answer: The 50 - ounce bottle has a cost of .0798 per ounce while the 100-ounce bottle has a cost of .0649 per ounce. The bigger bottle is a better buy.

Divide by a decimal Change the divisor to a whole number by moving the decimal point to the right, counting the places as you go. Use a caret ( ^ ) to show the new position of the decimal point. Move the decimal point in the dividend to the right as many places as you moved the divisor. Place the decimal point for the quotient directly above the new decimal point for the dividend. Divide as you would divide a whole number.

Try these examples. Without using your calculator) 12.3 ÷ .06 = 205 15 ÷ .004 = 3,750 20.765 ÷ .08 = 259.5625

Try these word problems. Bill Sullivan has an hourly rate of $14.32 and his gross weekly pay was $572.80. How many hours did he work? 40 hours Jan Stevens has an hourly rate of $7.75 per hour and her gross weekly pay was $193.75. How many hours did she work last week? 25 hours

3.3 Decimal and Fraction Conversions Convert a decimal to a fraction. Convert a fraction to a decimal. 1/2 = 50% 25% = 1/4

Convert a decimal to a fraction Find the denominator: write 1 followed by as many zeros as there are places to the right of the decimal point. Find the numerator: use the digits without the decimal point. Reduce to lowest terms and/or write as a whole or mixed number.

Here’s an example. Write 0.8 as a fraction “8” becomes the numerator. There is one place to the right of the decimal point: 1 + 0 = 10. “10” becomes the denominator. 0.8 = 8/10 Reduce to lowest terms. 4/5

Try these examples. ¾ ⅝ ¼ 0.75 converted to a fraction becomes…

Convert a fraction to a decimal Write the numerator as a dividend and the denominator as the divisor. Divide the numerator by the denominator, taking the division out as many decimal places as necessary or desirable. Note: In some cases, a repeating decimal will be the quotient of the operation. You may indicate that it is a repeating decimal or round as needed.

Here’s an example. Write ⅞ as a decimal. Divide 8 into 7.000. The result is 0.875 In this case the quotient is called a terminating decimal; there is no remainder.

Try these examples. Convert ½ to a decimal. 0.5 0.375 Convert ⅔ to a decimal. 0.6666(repeating) or 0.67