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# Decimals

Requirements in Math 501.

by

Tweet## BrylinGen Villarino

on 7 October 2012#### Transcript of Decimals

“Math is like love -- a simple idea but it can get complicated.” Decimals A linear array of digits that represents a real number, every decimal place indicating a multiple of a negative power of 10. Also called as, Decimal Fraction. Definition: It is a fraction that has a denominator of a power of ten, the power depending on or deciding the decimal place. Decimal Fraction The decimal, For example: A representation of a fraction or other real number using the base ten and consisting of any of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and a decimal point. Decimal Notation It is indicated by a decimal point to the left of the numerator, the denominator being omitted. Zeros are inserted between the point and the numerator, if necessary, to obtain the correct decimal place. 0.1 = 1/10

0.12 = 12/100

0.003 = 3/1000 To read decimal numbers remember that from left to right the digits to the right of the decimal point are: Naming a Decimal Example: Each digit to the left of the decimal point indicates a multiple of a positive power of ten, while each digit to the right indicates a multiple of a negative power of ten. To separate the negative and positive exponents of the base, a decimal point is used which is also called a separatrix. 0.23 = twenty-three hundredths

5.2 = five and two tenths We use the word "and" to separate the whole number and decimal

34.00021 = thirty-four and twenty-one hundred-thousandths Write down the word for: Exercises: A. 0.542 = B. 4.02 = Write down the decimal for: A. three thousandths = B. five and twenty-one hundredths = ANSWER: A. 0.542 = Five-Hundred Forty-Two Thousandths B. 4.02 = Four and Two Hundredths A. three thousandths = 0.003 B. five and twenty-one hundredths = 5.21 Write down the word for: Write down the decimal for: Expressing Decimals to Fractions and vice versa To change a fraction to a decimal, we count the number of zeros in the denominator. This number is the number of digits to the right of the decimal place. Changing from Fractions to Decimals Example 3/10 = 0.3

59/100 = 0.59

5/1000 = 0.005 To convert a decimal to a fraction, we put the decimal part, we count the number of digits to the left of the decimal place. Then we place the left of the decimal over 1 with this many zeros. Finally reduce if possible Converting Decimals to Fractions Examples: 0.4 = 4/10 = 2/5

2.1 = 2 1/10

3.55 = 3 55/100 = 3 11/20 Kinds of Decimals Finite decimals are the easiest to comprehend. A percentage, for instance, is an example. If you say 37 percent, you are saying 37 out of 100, or 0.37. You may even extend the percentage further. For example, 37.42 percent is simply 0.3742. These decimals end, unlike the other kinds, which extend forever. Common decimals are 0.5, equal to one-half, or 0.125, which equals one-eighth. Each place rightward of the decimal is a power of 10. The first place, thus, is 1/10, followed by 1/100, 1/1,000, 1/10,000.

Read more: Three Kinds of Decimals | eHow.com http://www.ehow.com/info_8458106_three-kinds-decimals.html#ixzz28M0h5r2BRounding up means that we increase the terminating digit by a value of 1 and drop off the digits to the right. If the next place beyond where we are terminating the decimal is greater than or equal to five, we round up. For example, if we round 5.47 to the tenths place, it can be can be rounded up to 5.5. Finite Decimals You will encounter repeating decimals when you do a division problem of a particular type. As an example, divide 100 by 3. The result is 33.3333, the "3" repeating over and over. The only way to work with a decimal like this is to choose where to stop and round it off. Here, rounded off to two digits, the result is 33.33. Sometimes these numbers render more cleanly as fractions. The decimal 0.333 (repeating) is really just one-third.

Read more: Three Kinds of Decimals | eHow.com http://www.ehow.com/info_8458106_three-kinds-decimals.html#ixzz28M1e8yqa Repeating Decimals Irrational decimals arise from other mathematical operations, like square roots. They go on infinitely, but do not repeat. The square root of 5, for instance, starts as 2.23606, and continues rightward without repeating. The number pi, used for calculations with circles, is another common irrational decimal.

Read more: Three Kinds of Decimals | eHow.com http://www.ehow.com/info_8458106_three-kinds-decimals.html#ixzz28M2RewyR Irrational Decimals Rounding off a decimal is a technique used to estimate or approximate values. Rounding is most commonly used to limit the amount of decimal places. Instead of having a long string of decimals places, or even one that goes on forever, we can approximate the value of the decimal to a specified decimal place. Rounding off Decimals Rounding up means that we increase the terminating digit by a value of 1 and drop off the digits to the right. If the next place beyond where we are terminating the decimal is greater than or equal to five, we round up. For example, if we round 5.47 to the tenths place, it can be can be rounded up to 5.5. When to Round Up If the number to the right of our terminating decimal place is four or less (4, 3, 2, 1, 0), we round down. This is done by leaving our last decimal place as it is given and discarding all digits to its right. For example, if we round 6.734 to the hundredths place, it can be rounded down to 6.73. When to Round Down Example: Round 0.24 to the tenths place. The answer here is 0.2. We wish to round 0.24 to the tenths place. That means we only want one digit to appear after the decimal point, so .24 will round to .2 or .3, whichever is closer. There is a 4 in the hundredths place. Since this is less than 5, we round down, meaning we leave the 2 in the tenths place and drop the 4 off the end. Example #2: We wish to round 12.756 to the tenths place. That means we only want one digit to appear after the decimal point. In this example, there are two digits that appear to the right of the tenths place. Round 12.756 to the tenths place. The number 12.756 should be rounded up to 12.8. When rounding off 12.756, look only at the digit in the place directly to the right of the tenths place (the hundredths place). Check to see if the digit in the hundredths place is 5 or greater or less than 5. In this case the digit in the hundredths place is a 5, therefore we round up from 7 to 8. Fundamental Operation of Decimals Adding and Subtracting Decimals Addition and subtraction of decimals is like adding and subtracting whole numbers. The only thing we must remember is to line up the place values correctly. The easiest way to do that is to line up the decimal points.

In this section we will provide a few examples to remind you of the procedure for adding and subtracting decimals. Look at the examples below, and then read through the detailed examples. Example: Here is an example of adding 12.35 and 5.287. Notice how the decimal points are lined up. Here is an example of subtracting 2.28 from 12.993. Notice how the decimal points are lined up. Multiplication of Decimals When multiplying numbers with decimals, we first multiply them as if they were whole numbers. Then, the placement of the number of decimal places in the result is equal to the sum of the number of decimal places of the numbers being multiplied. For example, if we multiply 2.3 times 4.5, each number has one digit to the right of the decimal, so each has one decimal place. When they are multiplied, the result will have two digits to the right of the decimal, or two decimal places. Now let's look at a detailed example of multiplying two number with decimals. Detail Example: Detailed Example: Add the following numbers 1.19 and .16

The answer to this is: 1.19 + .16 = 1.35. First line the numbers up in a column, lining up the decimal points. Add down the columns, starting at the right. Notice that 9 + 6 = 15, so we need to carry a 1 to the tenths column. Continue to add down the columns, moving from right to left. Subtraction Subtract 1.387 from 12.17.

The answer to this is: 12.17 - 1.387 = 10.783 First line the numbers up in a column, lining up the decimal points. Since the number 1.387 has three digits after the decimal point, we add a zero on the end of 12.17 so it also has three digits showing past the decimal point. Subtract down the columns, starting at the right. Notice that in the thousandths column 7 > 0. We must "borrow" from the hundredths column. When we move to the hundredths column, we notice that 8 > 6. We must "borrow" from the tenths column. Continue to subtract down the columns, moving from right to left. Again, we need to borrow from the ones place to be able to subtract the tenths. Multiply 12.3 by 3.54.The answer is 43.542 When multiplying multi-digit numbers, we start with the digit at the furthest right of the bottom number and multiply that by each of the digits of the top number. Multiply the second digit from the right of the bottom number by the top. Notice how this second number is offset below the first. Do this for each digit of the bottom number, moving from right to left. Continue doing this for each digit of the bottom number, moving from right to left. Remember to offset each number as you multiply. Now add the numbers up going down the columns. To determine how many digits are to the right of the decimal point in the result, we count the decimal places in the two numbers being multiplied and add these together. Addition

Full transcript0.12 = 12/100

0.003 = 3/1000 To read decimal numbers remember that from left to right the digits to the right of the decimal point are: Naming a Decimal Example: Each digit to the left of the decimal point indicates a multiple of a positive power of ten, while each digit to the right indicates a multiple of a negative power of ten. To separate the negative and positive exponents of the base, a decimal point is used which is also called a separatrix. 0.23 = twenty-three hundredths

5.2 = five and two tenths We use the word "and" to separate the whole number and decimal

34.00021 = thirty-four and twenty-one hundred-thousandths Write down the word for: Exercises: A. 0.542 = B. 4.02 = Write down the decimal for: A. three thousandths = B. five and twenty-one hundredths = ANSWER: A. 0.542 = Five-Hundred Forty-Two Thousandths B. 4.02 = Four and Two Hundredths A. three thousandths = 0.003 B. five and twenty-one hundredths = 5.21 Write down the word for: Write down the decimal for: Expressing Decimals to Fractions and vice versa To change a fraction to a decimal, we count the number of zeros in the denominator. This number is the number of digits to the right of the decimal place. Changing from Fractions to Decimals Example 3/10 = 0.3

59/100 = 0.59

5/1000 = 0.005 To convert a decimal to a fraction, we put the decimal part, we count the number of digits to the left of the decimal place. Then we place the left of the decimal over 1 with this many zeros. Finally reduce if possible Converting Decimals to Fractions Examples: 0.4 = 4/10 = 2/5

2.1 = 2 1/10

3.55 = 3 55/100 = 3 11/20 Kinds of Decimals Finite decimals are the easiest to comprehend. A percentage, for instance, is an example. If you say 37 percent, you are saying 37 out of 100, or 0.37. You may even extend the percentage further. For example, 37.42 percent is simply 0.3742. These decimals end, unlike the other kinds, which extend forever. Common decimals are 0.5, equal to one-half, or 0.125, which equals one-eighth. Each place rightward of the decimal is a power of 10. The first place, thus, is 1/10, followed by 1/100, 1/1,000, 1/10,000.

Read more: Three Kinds of Decimals | eHow.com http://www.ehow.com/info_8458106_three-kinds-decimals.html#ixzz28M0h5r2BRounding up means that we increase the terminating digit by a value of 1 and drop off the digits to the right. If the next place beyond where we are terminating the decimal is greater than or equal to five, we round up. For example, if we round 5.47 to the tenths place, it can be can be rounded up to 5.5. Finite Decimals You will encounter repeating decimals when you do a division problem of a particular type. As an example, divide 100 by 3. The result is 33.3333, the "3" repeating over and over. The only way to work with a decimal like this is to choose where to stop and round it off. Here, rounded off to two digits, the result is 33.33. Sometimes these numbers render more cleanly as fractions. The decimal 0.333 (repeating) is really just one-third.

Read more: Three Kinds of Decimals | eHow.com http://www.ehow.com/info_8458106_three-kinds-decimals.html#ixzz28M1e8yqa Repeating Decimals Irrational decimals arise from other mathematical operations, like square roots. They go on infinitely, but do not repeat. The square root of 5, for instance, starts as 2.23606, and continues rightward without repeating. The number pi, used for calculations with circles, is another common irrational decimal.

Read more: Three Kinds of Decimals | eHow.com http://www.ehow.com/info_8458106_three-kinds-decimals.html#ixzz28M2RewyR Irrational Decimals Rounding off a decimal is a technique used to estimate or approximate values. Rounding is most commonly used to limit the amount of decimal places. Instead of having a long string of decimals places, or even one that goes on forever, we can approximate the value of the decimal to a specified decimal place. Rounding off Decimals Rounding up means that we increase the terminating digit by a value of 1 and drop off the digits to the right. If the next place beyond where we are terminating the decimal is greater than or equal to five, we round up. For example, if we round 5.47 to the tenths place, it can be can be rounded up to 5.5. When to Round Up If the number to the right of our terminating decimal place is four or less (4, 3, 2, 1, 0), we round down. This is done by leaving our last decimal place as it is given and discarding all digits to its right. For example, if we round 6.734 to the hundredths place, it can be rounded down to 6.73. When to Round Down Example: Round 0.24 to the tenths place. The answer here is 0.2. We wish to round 0.24 to the tenths place. That means we only want one digit to appear after the decimal point, so .24 will round to .2 or .3, whichever is closer. There is a 4 in the hundredths place. Since this is less than 5, we round down, meaning we leave the 2 in the tenths place and drop the 4 off the end. Example #2: We wish to round 12.756 to the tenths place. That means we only want one digit to appear after the decimal point. In this example, there are two digits that appear to the right of the tenths place. Round 12.756 to the tenths place. The number 12.756 should be rounded up to 12.8. When rounding off 12.756, look only at the digit in the place directly to the right of the tenths place (the hundredths place). Check to see if the digit in the hundredths place is 5 or greater or less than 5. In this case the digit in the hundredths place is a 5, therefore we round up from 7 to 8. Fundamental Operation of Decimals Adding and Subtracting Decimals Addition and subtraction of decimals is like adding and subtracting whole numbers. The only thing we must remember is to line up the place values correctly. The easiest way to do that is to line up the decimal points.

In this section we will provide a few examples to remind you of the procedure for adding and subtracting decimals. Look at the examples below, and then read through the detailed examples. Example: Here is an example of adding 12.35 and 5.287. Notice how the decimal points are lined up. Here is an example of subtracting 2.28 from 12.993. Notice how the decimal points are lined up. Multiplication of Decimals When multiplying numbers with decimals, we first multiply them as if they were whole numbers. Then, the placement of the number of decimal places in the result is equal to the sum of the number of decimal places of the numbers being multiplied. For example, if we multiply 2.3 times 4.5, each number has one digit to the right of the decimal, so each has one decimal place. When they are multiplied, the result will have two digits to the right of the decimal, or two decimal places. Now let's look at a detailed example of multiplying two number with decimals. Detail Example: Detailed Example: Add the following numbers 1.19 and .16

The answer to this is: 1.19 + .16 = 1.35. First line the numbers up in a column, lining up the decimal points. Add down the columns, starting at the right. Notice that 9 + 6 = 15, so we need to carry a 1 to the tenths column. Continue to add down the columns, moving from right to left. Subtraction Subtract 1.387 from 12.17.

The answer to this is: 12.17 - 1.387 = 10.783 First line the numbers up in a column, lining up the decimal points. Since the number 1.387 has three digits after the decimal point, we add a zero on the end of 12.17 so it also has three digits showing past the decimal point. Subtract down the columns, starting at the right. Notice that in the thousandths column 7 > 0. We must "borrow" from the hundredths column. When we move to the hundredths column, we notice that 8 > 6. We must "borrow" from the tenths column. Continue to subtract down the columns, moving from right to left. Again, we need to borrow from the ones place to be able to subtract the tenths. Multiply 12.3 by 3.54.The answer is 43.542 When multiplying multi-digit numbers, we start with the digit at the furthest right of the bottom number and multiply that by each of the digits of the top number. Multiply the second digit from the right of the bottom number by the top. Notice how this second number is offset below the first. Do this for each digit of the bottom number, moving from right to left. Continue doing this for each digit of the bottom number, moving from right to left. Remember to offset each number as you multiply. Now add the numbers up going down the columns. To determine how many digits are to the right of the decimal point in the result, we count the decimal places in the two numbers being multiplied and add these together. Addition