3-1 Representing Decimals
Use your place value chart to write a decimal in word or expanded form (and vice versa). Example:
Write 6.23 in word and expanded form. (Image: math.tutorvista.com)
Word form: "Six AND twenty- three hundredths"
Expanded form: (6 x 1) + (2 x 0.1) + (3 x 0.01) ---> How'd we get that? We multiplied each digit by the number that represents the place value it's in. For example, since the 2 is in the "tenths" place, and one tenth is represented by "0.1," we multiplied them together to get the 2 tenths we need.
3-2 Comparing & Ordering Decimals
1) Line the decimals up
2) Annex zeros if neccessary
3) Go down each column and compare the numbers in each place value with each other
*See p.109 in your textbook for a great picture of this
3-3 Rounding Decimals
To round:
1) Underline the digit to be rounded (if you need to round to the nearest tenth, underline the digit that's in the tenths place)
2) Look at the number to the right - "5 and above, give it a shove; 4 and below, let it go" - so the digit that's being rounded goes up one if a 5 or above is to the right, and stays the same if a 4 or below is to the right.
3) Drop the rest of the numbers. Your new number should end at the place value you needed to round to.
Example: Round 7.35 to the nearest tenth.
First, underline the digit in the tenths place: 7.35
Now, look @ the number to the right: 7.35
It's 5 or above, so we give the 3 a shove: 7.4 (notice that the new number ends at the spot we had to round to)
3-4 Estimating Sums & Differences
I know this section is a little confusing, but keep in mind we're learning how to round just so we can check our real answers to see if they're reasonable.
Estimation Methods
Rounding: Estimate by rounding each decimal to the nearest whole number that's easy for you to add or subtract mentally.
Front-End Estimation: Add or subtract the front digits. Then add or subtract the next digits.
Clustering: Round a group of close numbers to the same number.
*Once you've rounded the decimals, don't forget to add or subtract!!!
3-5 Adding and Subtracting Decimals
1) Line up the decimal points and carry the decimal down.
2) Add or subtract just like with whole numbers.
*Remember to add zeros if you need to.
Here's an example from edu320.pbworks.com. In the second problem, we could add zeros to 4.1 if it makes it easier to add/subtract. It would then look like "4.100".
Tomorrow we'll practice adding and subtracting.
