Presentation on theme: "MSJC ~ San Jacinto Campus Math Center Workshop Series"— Presentation transcript:
1MSJC ~ San Jacinto Campus Math Center Workshop Series DECIMAL NUMBERSMSJC ~ San Jacinto CampusMath Center Workshop SeriesJanice Levasseur
2MSJC ~ San Jacinto Campus Math Center Workshop Series DECIMAL NUMBERSMSJC ~ San Jacinto CampusMath Center Workshop SeriesJanice Levasseur
3Introduction to Decimal Numbers A number written in decimal notation has 3 parts:Whole # partThe decimal pointDecimal partThe position of the digit in the decimal number determines the digit’s value.
4Place Value Chart Whole number part Decimal part Decimal point . 103 10210110010-110-210-310-410-5tensonestenthsthousandshundredshundredthsthousandthsten-thousandthsHundred-thousandthsWhole number partDecimal partDecimal point
5Writing a Decimal Number in Words Write the whole number partThe decimal point is written “and”Write the decimal part as if it were a whole numberWrite the place value of the last non-zero digitEx: Write 6.32 in wordsSixandthirty-twohundredths
6Ex: Write 0.276 in words Ex: Write 10.0304 in words Zero and two hundred seventy-sixthousandthsOr two hundred seventy-six thousandthsEx: Write in wordsTenandthree hundred fourTen-thousandths
7Writing Decimal Numbers in Standard Form Write the whole number partReplace “and” with a decimal pointWrite the decimal part so that the last non-zero digit is in the identified decimal place valueNote: if there is no “and”, then the number has no whole number part.
8Ex: Write in standard form “seven hundred sixty-two thousandths” Ex: Write in standard form “eight and three hundred four ten-thousandths”8.Ex: Write in standard form “seven hundred sixty-two thousandths”Note: no “and” no whole part0 .
9Converting Decimal to Fractions To convert a decimal number to a fraction, read the decimal number correctly. Simplify, if necessary.Ex: Write 0.4 as a fraction0.4 is read “four tenths”Ex: Write 0.05 as a fraction0.05 is read “five hundredths”
100.007 is read “seven thousandths” Ex: Write as a fraction0.007 is read “seven thousandths”Note: the number of decimal places is the same as the number of zeros in the power of ten denominatorEx: Write 4.2 as a fractional numberNote: there’s a whole and decimal part Mixed number4.2 is read “four and two tenths”4
12Converting Fractions to Decimal Numbers (base 10 denominator) When the fraction has a power of 10 in the denominator, we read the fraction correctly to write it as a decimal numberEx: Write as a decimal numberThe fraction is read “three tenths”Note: no “and” no whole part0 .3
13. Ex: Write as a decimal number The fraction is read “twenty-seven hundredths”Note: no “and” no whole part0 .Ex: Write as a decimal numberThe mixed number is read “five and thirty-three thousandths”.5
14Converting fractions to decimals, take the numerator and divide by the denominator. If the fraction is a mixed number, put the whole number before the decimal.Rewrite as long division.
15Ex: Write as a decimal number .83365. 0Place a bar over the part that repeats.21 85/6= 0.8321 82Is there an echo?This will repeat repeating decimal number
16Ex: Convert to a decimal Notice the mixed number – whole & fraction part The decimal number will have a whole & decimal partThe whole part is 2 2 . ________Now convert the fraction 5/8 to determine the decimal part:.6252 5/8= 2.62585. 04 821 644 0
18Rounding Decimal Numbers Rounding decimal numbers is similar to rounding whole numbers:Look at the digit to the right of the given place value to be rounded.If the digit to the right is > 5, then add 1 to the digit in the given place value and zero out all the digits to the right (“hit”).If the digit to the right is < 5, then keep the digit in the given place value and zero out all the digits to the right (“stay”).
19Ex: Round 7.359 to the nearest tenths place Identify the place to be rounded to:TenthsLook one place to the right. What number is there?Compare the number to 5: 5 > 5 “hit” (add 1)3 + 1 = 4 in the tenths place, zero out the rest7.359 rounded to the nearest tenths place is7.400 = 7.4
20Ex: Round 22.68259 to the nearest hundredths place Identify the place to be rounded to:HundredthsLook one place to the right. What number is there?Compare the number to 5: 2 < 5 “stay” (keep)Keep the 8 and zero out the restrounded to the nearest hundredths place is = 22.68
21Ex: Round 1.639 to the nearest whole number Identify the place to be rounded to:onesLook one place to the right. What number is there?Compare the number to 5: 6 > 5 “hit” (add 1)1 + 1 = 2 in the ones place, zero out the rest1.639 rounded to the whole number is2.000 = 2
23Decimal Addition & Subtraction To add and subtract decimal numbers, use a vertical arrangement lining up the decimal points (which in turn lines up the place values.)Ex: Addput in 0 place holders16.11315.21+2.003633.3266
24put in the decimal point 16 . 0000 - 9.6413 put in 0 place holders Ex: Subtract – 19.61113124.024put in 0 place holders-19.614.414Ex: Subtract 16 –199951put in the decimal point16.0000-9.6413put in 0 place holders6.3587
26Decimal Multiplication Decimal numbers are multiplied as if they were whole numbers. The decimal point is placed in the product so that the number of decimal places in the product is equal to the sum of the decimal places in the factors.
27Ex: Multiply 1.2 x 0.04Think 12 x 4 12 x 4 = 481.2 has 1 decimal place0.04 has 2 decimal placesTherefore the product of 1.2 and 0.04 will have = 3 decimal places48. 1.2 x 0.04 = 0.048
28Ex: Multiply 3.1 x 1.45Think 31 x 145 31 x 145 =44953.1 has 1 decimal place1.45 has 2 decimal placesTherefore the product of 3.1 and 1.45 will have = 3 decimal places. 3.1 x 1.45 = 4.495
29Multiply by Powers of 10 When multiplying by 10, 100, 1000, … Move the decimal in the number to the right as many times as there are zeros.2.345 times 10, move the decimal one place to the right, 23.45
30Ex: Multiply x 10Think x 10 x 10 =has 4 decimal place10 has 0 decimal placesTherefore the product of and 10 will have = 4 decimal places123450. x 10 ==
31Ex: Multiply x 100Think x 100 x 100 =has 4 decimal place100 has 0 decimal placesTherefore the product of and 100 will have = 4 decimal places. x 100 ==
32Ex: Multiply x 1000Think x 1000 x 1000 =has 4 decimal place1000 has 0 decimal placesTherefore the product of and 1000 will have = 4 decimal places. x 1000 ==
33So what have we seen?x 10 =1 zero move decimal point 1 place to the rightx 100 =2 zeros move decimal point 2 places to the rightx 1000 =3 zeros move decimal point 3 places to the rightTo multiply a decimal number by a power of 10, move the decimal point to the right the same number of places as there are zeros.
34Ex: Multiply x 1000How many zeros are there in 1000?3 Move the decimal point in to the right 3 times34.31. x 1000 = 34,310
35Ex: Multiply 21 x 100How many zeros are there in 100?2 Move the decimal point in to the right 2 times21.. 21 x 100 = 2100
37Decimal DivisionTo divide decimal numbers, move the decimal point in the divisor to the right to make the divisor a whole number.Move the decimal point in the dividend the same number of places to the right.Place the decimal point in the quotient directly over the decimal point in the dividend.Divide like with whole numbers.
38Ex: Set up the division of 0.85 0.5 .5.85Why does this work?Multiplication Property of One, “Magic One”Consider the fraction representation of the division:Which is the equivalent division we get after moving the decimal point.
41Ex: Divide 37.042 0.76, round to the nearest tenth. When dividing decimals, we usually have to round the quotient to a specified place value.Ex: Divide , round to the nearest tenth. the answer to the division (i.e. the rounded quotient) is 48.748.73.76374.26 645 623 0
42Divide by Powers of 10 When dividing by 10, 100, 1000, … Move the decimal in the number to the left as many times as there are zeros.76.89 divided 10, move the decimal one place to the left, 7.689
45So what have we seen?=1 zero move decimal point 1 place to the left=2 zeros move decimal point 2 places to the leftTo divide a decimal number by a power of 10, move the decimal point to the left the same number of places as there are zeros.