Reading Decimals Say what you see before the
Reading Decimals Say what you see before the decimal Say “and” for the decimal Say what you see after the decimal Say the place value of the final digit To write in words, you write what you say
five hundred eighty and 580 . 324 three hundred twenty-four thousandths
Ten thousands hundreds tens thousands ten thousandth s tenths ones Hundred thousandth s hundredths
One and forty-six hundredths
sixty seven and four thousand eighteen thousandths
Twelve thousand three hundred four and two thousandths
three and forty seven tenths three and forty seven hundredths Three and forty seven thousandths Three and forty seven hundred
seventeen and eighty-two tenths seventeen thousand eighty two seventeen and eighty-two hundredths seventeen and eighty-two thousandths
Zero and three thousand two ten thousandths three thousand two thousandths
Sixty four hundredths twenty one Sixty-four thousand twenty one Six hundred forty thousand twenty one millionths Six hundred forty thousand twenty one thousandths
Base Ten Blocks
One and four tenths
One and four tenths
Represents one whole bar Represents one hundredth of a bar (meaning you need one hundred to make a bar) Represents one tenth of a bar (meaning you need ten to make a bar) Represents one thousandth of a bar (meaning you need one thousand to make a bar)
One and seven hundredths
One and seven hundredths
Fifty-three hundredths
Fifty-three hundredths or 0. 53
One and two hundred forty-five thousandths
One and two hundred fortyfive thousandths or 1. 245
Six thousandths
Six thousandths or 0. 006
One and thirteen thousandths
One and thirteen thousandths or 1. 013
Two and one hundred seventythree thousandths or 2. 173
four hundred twenty-five thousandths or 0. 425
One and two hundred eightythree thousandths or 1. 283
Which is the larger value? 0. 129 or 0. 31 Prove your choice!
0. 129 0. 31 0. 129 is less than 0. 31, so 0. 31 is the largest value
Which is the larger value? 0. 2 or 0. 05 Prove your choice!
0. 2 0. 05 0. 2 is greater than 0. 05
Understanding Decimal Values 45. 076 45. 0076 673. 09 673. 1 1098. 44 1098. 4
1. Understanding Decimal Values 67. 7600 67. 76 0. 515 0. 551 15. 099 15. 98
nine out of ten 0. 9 nine tenths 9 10
four out of ten 0. 4 four tenths 4 10
two wholes and seven out of ten two and seven tenths 2. 7 2 7 3 1 0
Thirty-two out of one hundred 0. 32 thirty-two hundredths 32 100
eighty out of one hundred 0. 80 eighty hundredths 80 100
six out of one hundred 0. 06 six hundredths 6 100
Three wholes and two parts out of a hundred Three and two hundredths 3. 02 3 2 4 100
2 14 100 Two and fourteen hundredths 2. 14 Two wholes and fourteen out of one hundred
Decimals in Expanded Form Writing decimals in expanded form is an extension of whole numbers in expanded form. To do this you represent each individual place value EXAMPLE 4. 305 is 4 + 0. 3 + 0. 005 4 x 1 + 3 x 0. 1 + 5 x 0. 001 4 x 100 + 3 x 10 -1 + 5 x 10 -3
Decimals in Expanded Form 34. 308 30 + 4 + 0. 3 + 0. 008 3 x 10 + 4 x 1 + 3 x 0. 1 + 8 x 0. 001 3 x 101 + 4 x 100 + 3 x 10 -1 + 8 x 10 -3 5. 28 5 + 0. 2 + 0. 08 5 x 1 + 2 x 0. 1 + 8 x. 01 5 x 100 + 2 x 10 -1 + 8 x 10 -2
Decimals in Expanded Form 3 + 0. 4 + 0. 09 = 3. 49 9 x 101 + 3 x 10 -1 + 5 x 10 -2 = 40 + 0. 8 + 0. 003 = 0. 7 + 0. 03 + 0. 0002 = 90. 35 40. 803 0. 7302 0. 06 + 0. 4 + 3 + 20 + 0. 001 = 800 + 3 + 60 000 + 0. 02 + 0. 007 = 23. 461 60 803. o 27
Decimals in Expanded Form 4000. 53 4 x 1000 + 5 x 0. 1 + 3 x 0. 01 = 7 x 100 + 2 x 0. 1 + 5 x 1 + 8 x 0. 001 = 705. 208 4 x 0. 0001 + 3 x 0. 1 + 2 x 0. 01 = 0. 3204 0. 006 + 0. 01 + 700 + 20 + 0. 0004 = 720. 0164 3 x 1 + 4 x 0. 01 = 3. 04 8 x 100 + 5 x 10 -2 + 3 x 10 -3 = 8. 053
Rounding Decimals When rounding decimals it is first necessary to identify the place value you are rounding to. The digit that follows will tell you whether you should round up or leave the digit the same. If the digit is: l 5 or higher – round up by one If the digit is: l 4 or lower – leave the same Digits past the rounded digit are not recorded in the rounded number.
When rounding it is helpful if you. . . Circle the place value you are rounding to. Underline the digit that follows; it is this digit that tells you to round up or leave the same.
Example 34. 561 rounded to the nearest tenth is. . . 34. 561 34. 6
Example 4. 6341 rounded to the nearest hundredth is. . . 4. 6341 4. 63
Example 67. 1125 rounded to the nearest thousandths is 67. 1125 67. 113
Example. 6971 rounded to the nearest hundredth is. . . 0. 6971. 70
Example 5. 96 rounded to the nearest tenth is. . . 5. 96 6
Example 587. 469 rounded to the nearest whole number is. . . 587. 469 587
Example 7535. 9 rounded to the nearest whole number is. . . 7535. 9 7536
Example 619. 844 rounded to the nearest whole number is. . . 619. 844 620
Example 6198 rounded to the nearest hundred is. . . 6198 6200
Example 463 228 rounded to the nearest hundred thousand is. . . 463 228 500 000
8 x 0. 3 = 2. 4 Eight groups with three tenths in each group
2 x 1. 6 = 3. 2 Two groups with one and six tenths in each group
4 x 0. 9 = 3. 6 Four groups with nine tenths in each group
9 x 0. 5 = 4. 5 Nine groups with five tenths in each group
2 x 1. 2 = 2. 4 Two groups with one and two tenths in each group
Question # 9 Example To share 1. 7 of a bar I would need two bars. I would give away one whole bar and break the second bar into ten equal pieces and give away seven pieces of the ten or one and seven tenths. One and seven tenth as a fraction is 1 7 10
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