Week 1 · Reading, comparing and writing decimals to thousandths · 3 lessons
1
From milliards down to thousandths
Discover Mathematics P5: Term 1, Unit 1, Lessons 1–5
GoalRead and write numbers from billions down to thousandths and name the value of every digit.
New words
billion (milliard) · a thousand millions: 1,000,000,000decimal point · the dot that separates the ones place from the tenths placehundredth · one of 100 equal parts of a whole, written 0.01thousandth · one of 1,000 equal parts of a whole, written 0.001
Explanation
Whole-number places come in groups of three: ones, thousands, millions and billions (the book also says milliards). To the right of the ones place a decimal point starts the parts of one whole. The first place after the point is tenths (0.1), then hundredths (0.01), then thousandths (0.001). Every place is worth ten times the place to its right. In 3,052,408.619 the digit 6 is 6 tenths = 0.6, the digit 1 is 1 hundredth = 0.01 and the digit 9 is 9 thousandths = 0.009. To read it, say the whole part as usual, say “and” at the point, then read the digits after the point as one number and finish with the name of the last place: six hundred nineteen thousandths. Zeros must stay: 0.05 is five hundredths, not five tenths.
3,052,408.619
Millions
Thousands
Ones
Tenths
Hundredths
Thousandths
3
052
408
6
1
9
Worked examples
Thousands
Hundreds
Tens
Ones
Tenths
Hundredths
Thousandths
8
2
0
6
0
5
4
A water meter shows 8,206.054 L. Read it: eight thousand two hundred six and fifty-four thousandths. The 0 in the tenths place must be written, because without it the number would be 8,206.54, which is a different number.
Digit
3
9
6
8
Place
hundred thousands
Tenths
Hundredths
Thousandths
Value
300,000
0.9
0.06
0.008
In 5,304,271.968 the digit 3 is in the hundred thousands place, so it is worth 300,000. After the point the 9 is 9 tenths = 0.9, the 6 is 6 hundredths = 0.06 and the 8 is 8 thousandths = 0.008. Together 0.9 + 0.06 + 0.008 = 0.968.
Billions
Millions
Thousands
Ones
Tenths
Hundredths
4
050
000
000
0
7
Write “four billion, fifty million and seven hundredths” in digits. Four billion is 4,000,000,000 and fifty million is 50,000,000, so the whole part is 4,050,000,000. Seven hundredths puts the 7 in the hundredths place, and a 0 holds the tenths place: 4,050,000,000.07.
Class activity
Place-value mat. Draw six boxes in a row on paper and label them: hundreds, tens, ones, tenths, hundredths, thousandths (leave a small gap for the point after the ones box). Pick six number cards from 0 to 9 and place them in the boxes. Read the decimal you made aloud. Then the grown-up points at one digit and the child says what it is worth. Swap roles.
Practice
1
Write in digits: nine hundred twelve and four hundred seven thousandths.
912.407.
2
In 60,385.724 what is the value of the digit 8 and of the digit 2?
The 8 is in the tens place: 80. The 2 is in the hundredths place: 0.02.
3
Read 0.409 in words. Which place is the digit 4 in, and what is it worth?
Four hundred nine thousandths. The 4 is in the tenths place and is worth 0.4.
4
Omar writes “six hundredths” as 0.6. Correct him.
Six hundredths is 0.06. The number 0.6 is six tenths. A 0 must hold the tenths place.
5
How many thousandths make one hundredth? How many hundredths make one tenth?
10 thousandths make 1 hundredth, and 10 hundredths make 1 tenth, because each place is ten times the place to its right.
