Multiplying decimals by 10, 100 and 1000, explained on a place-value chart
A place-value chart with the point drawn as a fixed heavy line, and the digits moving past it: 3.7 becomes 37 when every digit steps one column left, 48 becomes 0.048 when every digit steps three columns right and the empty places are filled with noughts. The steps say what each digit is worth before and after, and six questions follow.
Read the chart: the digits move, the point stays. Then try the six below.
The digits move; the point stays
Times 10 makes every digit worth ten times more, so every digit moves one place to the left. The point never moves. Divide by 10 and every digit moves one place to the right. Think of a row of chairs: everyone shifts one seat along, and the seats stay where they are.
In the chart, Th H T O are thousands, hundreds, tens and ones; t h th are tenths, hundredths and thousandths. The heavy line is the point.
3.7 × 10 and 48 ÷ 1000, step by step
1.3.7 × 10. Ten times more: 3 ones become 3 tens; 7 tenths become 7 ones. Read it: 37. 37 is ten times the size of 3.7.
2.48 ÷ 1000. A thousand times smaller: three places right. 4 tens become 4 hundredths; 8 ones become 8 thousandths.
3.Fill the empty places with 0 so every column has a digit: 0.048. 0.048 is one-thousandth times the size of 48.
4.Check by going back: 0.048 × 1000 = 48.
3.7 × 10 =37
48 ÷ 1000 =0.048
For the grown-up: ask what the 7 is worth now — tenths — and what it will be worth after — ones. If they can say that, the answer writes itself.
Multiplying and dividing by 10, 100 and 1000
NameDate/ 6
Read the chart: the digits move, the point stays. Then try the six below.
1.6 ÷ 100 =
2.0.56 × 100 =
3.305 ÷ 1000 =
4.3.07 × 1000 =
5.4.2 × 10 =
6.25 ÷ 10 =
Multiplying and dividing by 10, 100 and 1000
NameDate/ 6
Read the chart: the digits move, the point stays. Then try the six below.
1.6 ÷ 100 =0.06
2.0.56 × 100 =56
3.305 ÷ 1000 =0.305
4.3.07 × 1000 =3070
5.4.2 × 10 =42
6.25 ÷ 10 =2.5
What is on this sheet
Move the decimal point is the rule most parents were taught, and it is not what this page says, for a reason that is worth a sentence. A digit one column to the left is worth ten times as much — that is what × 10 does — and a child who says the 7 was tenths and is now ones can explain the answer; a child who slid a point can only report it. The two pictures give the same answers, and the lesson does not call the other one wrong; it teaches the one that keeps a child saying what each digit is worth.
The division example is a whole number on purpose. 48 ÷ 1000 is the question a child who has only ever slid a point along a decimal has nowhere to start on, and the chart shows what happens: the 4 and the 8 step three columns right, and the ones and tenths columns are left empty until noughts are written in them, so the answer is 0.048 and not .48. The six to try mix decimals with whole numbers the same way, and run on to a second page.
The answers were worked out when the problems were, so the key is the same page with the answers drawn in rather than a second attempt at the same questions — there is no way for the two to disagree. The number in the footer is the seed the sheet was built from: it is printed so that the identical sheet can be had again next week, rather than one that merely looks like it.
Change what is on it
This page is one sheet out of a family that can print thousands, and the settings behind it — how many problems, how big the numbers get, how they are laid out, whether there is room to work — are all switches. The builder link at the top of the page carries this sheet’s own settings, so the bench opens on exactly the sheet here rather than on a blank one.
The configuration travels in the address bar rather than on a server, so the link can be bookmarked or sent to somebody as it stands — and what they open is this sheet, down to the seed, rather than another one like it.
The same facts, on screen
Not in the games. The ten times table underneath is, in The Grid.
