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Adding and Subtracting Fractions
Adding and Subtracting Mixed Numbers
Comparing and Ordering Decimals
Comparing and Ordering Numbers
Conversions Between Mixed and Improper Fractions
Dividing by 10,100, 100
Dividing Fractions and Mixed Numbers
Estimating Sums and Differences
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Forms For Writing Numbers
Standard form is when I write a number as a regular old number.
When we write a number using words we write each part as a one, two, or three digit number seperating each part or period with that periods name and a comma.
Here is an example: 123,456,789.123 is one hundred twenty-three million, four hundred fifty-six thousand, seven hundred eighty-nine and one hundred twenty-three thousandths.
Things to Remember:
means a decimal place.
Some people say and write 204 as two hundred and four. Two hundred and four means 200.4, which is quite a bit different.
If you just say or write the number in between the comma and then follow it by the periods name it always works.
Decimals in word form are easy. Just say or write the number that is made after the decimal place as if it were an ordinary number, and then end it with the place value that it ends in.
.123 would be written as one hundred twenty-three thousandths, because it end in the thousandths place. .0123 would be one hundred twenty-three ten-thousandths, because it end in the ten-thousandths place. .6= six tenths, .06= six hundredths, you get the picture.
Expanded Form is when you write the number out showing the number of carmels or ones in each place value.
An example would be... 123,456,789.123 in expanded form would look like 100000000 + 20000000 + 3000000 + 400000+ 50000+6000+ 700+ 80 + 9 + 1/10 + 2/100 + 3/1000.
If there is a zero in the number in standard form we just don't record that place value in expanded form.
An example would be... 123,400,789.103 in expanded form would look like 100000000 + 20000000 + 3000000 + 400000 +700 + 80 + 9 + 1/10 + 3/1000.
Expanded Form with Exponents
When you are writing decimals in expanded form with exponents it is the same as regular expanded form, except the long list of zeros for each place value is replaced by an exponent.
If I write 123,456,789.123 in expanded form using exponents it would look like (1• 10
) + (2• 10
) + (3• 10
) + (4• 10
) +(5• 10
) +(6• 10
) + (7• 10
) +(8• 10
) +(9• 10
) +(1• 10
) + (2 • 10
) + (3 • 10
Some important tips:
Remember the •10 before the exponent. 4•10
=400, but 4
The number in the exponent place is equal to the number of 0's the that number had when it was in regular expanded form. 40,000 has five 0's, so it would be written 4•10
Remember the ones place is shown as •10
Remember decimals are shown by using negative integers starting at •10
for the tenths place. The number .123 would be shown as (1•10
) + (2•10
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