Number Sense and Numeration

1. Number Sense and Numeration Quiz #1 recap

2. Rounding Numbers Now that we understand that parts of numbers have different place values, we can use that information to help us round numbers either up or down We can round numbers to the nearest ten, hundred, thousand, or ten thousand Remember, we look at the number to the right of the number we are rounding to decide what to do with it

3. Rounding Numbers (continued) If the number to the right of the number we are rounding (no matter what place value it is) is 5 or higher, we round up (the number increases by 1) and if it is 4 or lower, we round down (the number stays the same) For example, if you are asked to round to the nearest hundred, you will look at the number in the tens column to figure out what to do with the hundreds number Once you have figured out whether to round the number up or down, do that, but also remember to make all the numbers to the right of the rounded number into zeros

4. Practice with Rounding to Different Place Values Round this number to the nearest ten thousand:38 495 40 000 Now round it to the nearest thousand 38 000 Now round it to the nearest hundred 38 500 And lastly, round it to the nearest ten 38 500 ***notice that because the number in the tens column is a 9 and the number to the right of the 9 is a 5, we would round up, however, a 9 can only go up to a ten so we have to carry it over to the hundreds column, just like when we add***

5. More Practice with Rounding Round this number to the nearest ten thousand:164 934 160 000 Now round it to the nearest thousand 165 000 Now round it to the nearest hundred 164 900 And lastly, round it to the nearest ten 164 930

6. Important Terms STANDARD FORM – The way we usually write numbers (using numbers). When numbers greater than 9999 are written in standard form, the thousands part is separated from the rest of the number with a space to make it easier to read (e.g. 10 000) SPACE EXPANDED FORM – A way to write a number that shows the value of each digit (e.g. In expanded form, 2365 is 2000+300+60+5 or 2 thousands 3 hundreds 6 tens 5 ones.)

7. More Practice with Expanded Form Write the number 21 341 in expanded form 20 000 + 1 000 + 300 + 40 + 1 Write the number 50 120 in expanded form 50 000 + 100 + 20 Write the number 52 003 in expanded form 50 000 + 2 000 + 3 Write the number 19 456 in expanded form 10 000 + 9 000 + 400 + 50 + 6 Write the number 564 882 in expanded form 500 000 + 60 000 + 4 000 + 800 + 80 + 2

8. One More Important Term WRITTEN FORM – When you are asked to write a number “in words”, you have to write it out using words (e.g. 27 894 would be written in words as “twenty-seven thousand eight hundred ninety-four” Use hyphens (this symbol –) when you are writing a number that would normally be 2 numbers read together, like twenty-seven (27) or sixty-eight (68), we call these compound numbers

9. Writing Numbers in Words and Using the Word “and” The word “and” is only used when writing numbers with decimal points This is important because the “and” is actually used to tell us there is a decimal point in a number You should NOT use the word and when writing out whole numbers in words For example, the number 475 is written as:four hundred seventy-five ***don’t forget the hyphen for compound numbers!!*** 475 would NOT be written as:four hundred and seventy-five

10. Practice Writing Numbers in Words Write the number 8935 in words eight thousand nine hundred thirty-five Write the number 649 092 in words six hundred forty-nine thousand ninety-two Write the number 158 in words one hundred fifty-eight Write the number 7463 in words seven thousand four hundred sixty-three Write the number 16 961 in words sixteen thousand nine hundred sixty-one

11. Practice Writing Numbers in Words using Decimal Numbers Write the number 8935.67 in words eight thousand nine hundred thirty-five andsixty-seven hundredths Write the number 649 092.9 in words six hundred forty-nine thousand ninety-two andnine tenths Write the number 158.95 in words one hundred fifty-eight andninety-five hundredths Write the number 7463.15 in words seven thousand four hundred sixty-three and fifteen hundredths Write the number 16 961.346 in words sixteen thousand nine hundred sixty-one and three hundred forty-six thousandths

12. Writing Numbers vs. Saying Numbers Please remember that writing numbers follows a different formula than saying them, especially when those numbers use decimals We would not read the number 16 961.346 as “sixteen thousand nine hundred sixty-one and three hundred forty-six”, we would read it as “sixteen thousand nine hundred sixty-one decimal three four six”