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

Twelve thousand three hundred four and 12 304 . 002 Twelve thousand three hundred four and two 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

0. 640021 Sixty four hundredths twenty one Six hundred forty thousand twenty one millionths 0. 640021 Six hundred forty thousand twenty one thousandths Sixty-four thousand twenty one

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

One and thirteen thousandths 1.013 One and thirteen thousandths

One and thirteen thousandths or 1.013

Two and one hundred seventy-three thousandths or 2.173

four hundred twenty-five thousandths or 0.425

One and two hundred eighty-three thousandths or 1.283

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  

Decimals in Expanded Form

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 3.49 3 + 0.4 + 0.09 = 9 x 101 + 3 x 10-1 + 5 x 10-2 = 40 + 0.8 + 0.003 = 0.7 + 0.03 + 0.0002 = 0.06 + 0.4 + 3 + 20 + 0.001 = 800 + 3 + 60 000 + 0.02 + 0.007 = 90.35 40.803 0.7302 23.461 60 803.o27

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 = 4 x 0.0001 + 3 x 0.1 + 2 x 0.01 = 0.006 + 0.01 + 700 + 20 + 0.0004 = 3 x 1 + 4 x 0.01 = 8 x 100 + 5 x 10-2 + 3 x 10-3 = 705.208 0.3204 720.0164 3.04 8.053

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