Understanding Decimal Numbers
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 5 8 0 . 3 2 4 three hundred twenty-four thousandths
20 759 . 16384 Hundred thousandths Ten thousands ten thousandths hundreds 20 759 . 16384 tens tenths thousandths ones thousands hundredths
1 . 46 One and forty-six hundredths
four thousand eighteen ten thousandths 67 . 4018 sixty seven and four thousand eighteen ten thousandths
3 . 47 three and forty seven tenths Three and forty seven thousandths three and forty seven hundredths Three and forty seven hundred
17 . 082 seventeen seventeen and eighty-two tenths and eighty-two hundredths 17 . 082 seventeen thousand eighty two seventeen and eighty-two thousandths
0 . 3002 Zero and three thousand two three thousand two ten thousandths 0 . 3002 three thousand two three thousand two thousandths
Modelling Decimal Numbers
Base Ten Blocks
1 . 4 One and four tenths
One and four tenths
one thousandth of a bar (meaning you Represents one whole bar Represents one tenth of a bar (meaning you need ten to make a bar) Represents one hundredth of a bar (meaning you need one hundred to make a bar) Represents one thousandth of a bar (meaning you need one thousand to make a bar)
1.07 One and seven hundredths
One and seven hundredths
0.53 Fifty-three hundredths
Fifty-three hundredths or 0.53
One and two hundred forty-five thousandths 1.245 One and two hundred forty-five thousandths
One and two hundred forty-five thousandths or 1.245
0.006 Six thousandths
Six thousandths or 0.006
Comparing Decimal Numbers
Which is the larger value? 0.129 or 0.31 Prove your choice!
0.129 0.129 is less than 0.31, so 0.31 is the largest value 0.31
Which is the larger value? 0.2 or 0.05 Prove your choice!
0.2 0.2 is greater than 0.05 0.05
Understanding Decimal Values 45.0076 45.076 673.09 673.1 1098.44 1098.4
1. Understanding Decimal Values 67.76 67.7600 0.515 0.551 15.099 15.98
Making Connections
nine out of ten nine tenths 0.9 9 10
four tenths four out of ten 0.4 4 10
two wholes and seven out of ten 7 10 two wholes and seven out of ten 2.7 two and seven tenths
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 and two hundredths Three and two hundredths 3.02 2 100 Three wholes and two parts out of a hundred
Two and fourteen hundredths 2 14 100 Two and fourteen hundredths 2.14 Two wholes and fourteen out of one hundred
Rounding Decimals
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: 5 or higher – round up by one 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 . . . 3 4 . 5 6 1 34.6
Example 4 . 6 3 4 1 4.6341 rounded to the nearest hundredth is . . .
Example 6 7 . 1 1 2 5 67.1125 rounded to the nearest thousandths is 67.113
Example 0 . 6 9 7 1 .6971 rounded to the nearest hundredth is . . . .70
Example 5.96 rounded to the nearest tenth is . . . 5 . 9 6 6
Example 587.469 rounded to the nearest whole number is . . . 5 8 7 . 4 6 9 587
Example 7535.9 rounded to the nearest whole number is . . . 7 5 3 5 . 9 7536
Example 619.844 rounded to the nearest whole number is . . . 6 1 9 . 8 4 4 620
Example 6198 rounded to the nearest hundred is . . . 6 1 9 8 6200
Example 463 228 rounded to the nearest hundred thousand is . . . 463 228 500 000
Multiplying Decimals
Eight groups with three tenths in each group 8 x 0.3 = 2.4 Eight groups with three tenths in each group
Two groups with one and six tenths in each group 3.2 Two groups with one and six tenths in each group
Four groups with nine tenths in each group 4 x 0.9 = 3.6 Four groups with nine tenths in each group
Nine groups with five tenths in each group 9 x 0.5 = 4.5 Nine groups with five tenths in each group
Two groups with one and two 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